This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In an exponential function like y = $a·b^x$, the parameter a is the initial value (what y equals when x = 0, since $b^0$ = 1), and the base b is the growth factor (if b > 1) or decay factor (if 0 < b < 1)—if b = 1.05, that means multiplying by 1.05 each time, which is a 5% increase! In the function N(t) = $300(1.10)^t$, the 300 is the initial value (starting number of bacteria of 300 when t=0), and the base 1.10 means the number is multiplied by 1.10 each hour—since 1.10 = 1 + 0.10, this represents 10% growth per hour; each hour, the number of bacteria is 10% larger than the hour before! Choice B is correct because it properly identifies that 1.10 represents the growth factor with the correct 10% increase interpretation. Choice D gets the direction wrong, saying decreases when actually it increases—with exponential functions, if b > 1 it's growth (getting bigger), if 0 < b < 1 it's decay (getting smaller); check whether your base is above or below 1! Quick check for exponential: if the base b = 1.10, think '1 plus 0.10, so that's 10% growth'; if b = 0.90, think '1 minus 0.10, so that's 10% decay'—the distance from 1 is the rate, and whether it's above or below 1 tells you growth or decay!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In an exponential function like y = $a·b^x$, the parameter a is the initial value (what y equals when x = 0, since $b^0$ = 1), and the base b is the growth factor (if b > 1) or decay factor (if 0 < b < 1). If b = 1.05, that means multiplying by 1.05 each time, which is a 5% increase! The base 0.85 means multiply by 0.85 each year, and since 0.85 = 1 - 0.15, this represents a 15% decrease per year. We subtract 0.85 from 1 to find the decay rate: 1 - 0.85 = 0.15 = 15%. Choice B is correct because it properly identifies that 0.85 represents keeping 85% of the value each year (a 15% decrease per year). Perfect! Choice C gets the direction wrong, saying increases when actually it decreases. With exponential functions, if b > 1 it's growth (getting bigger), if 0 < b < 1 it's decay (getting smaller). Check whether your base is above or below 1! For exponential functions y = $a·b^x$: a is what you have at time zero (plug in x = 0 and you get a), and b tells you the multiplication factor each time period. To find the percent rate: subtract 1 from b if b > 1 (like 1.05 → 0.05 = 5% growth), or subtract b from 1 if b < 1 (like 0.85 → 1 - 0.85 = 0.15 = 15% decay). Quick check for exponential: if the base b = 1.03, think '1 plus 0.03, so that's 3% growth.' If b = 0.97, think '1 minus 0.03, so that's 3% decay.' The distance from 1 is the rate, and whether it's above or below 1 tells you growth or decay!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function T = 4n + 12, the slope 4 represents the rate of $4 per movie rented, and the y-intercept 12 represents a $12 flat monthly fee. So the full story is: you pay $12 per month plus $4 for each movie rented. Choice B is correct because it properly identifies that 4 represents the cost increase of $4 per movie rented. Perfect! Choice A confuses the slope with the y-intercept: the 4 is actually the slope, which represents the rate per movie. It's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! For linear functions y = mx + b in context: m is always the rate (the 'per' something amount—$4 per movie), and b is always the starting value (the amount when x = 0—$12 monthly fee). If you can identify what's changing at a constant rate (that's m) vs what's there from the beginning (that's b), you've got it!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function C = 60w + 20, the slope 60 represents calories burned per mile (60 calories per mile walked), and the y-intercept 20 represents calories burned when 0 miles are walked (20 calories burned just from the activity of preparing to walk or baseline metabolism). So the full story is: you burn 20 calories as a baseline plus 60 calories for each mile you walk. Choice B is correct because it properly identifies that 60 is calories burned per mile (the rate), and 20 is the calories burned when 0 miles are walked (the starting value). Perfect! Choice A confuses the slope with the y-intercept (has them swapped): the 60 is actually the rate per mile (slope), and 20 is the starting value (y-intercept). It's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! For linear functions y = mx + b in context: m is always the rate (the 'per' something amount—$5 per item, 60 miles per hour), and b is always the starting value (the amount when x = 0—$20 initial fee, 50 degrees starting temperature). In context, always state the full interpretation with units: don't just say 'the slope is 60'—say 'the slope is 60 calories per mile, meaning each additional mile burns 60 calories.' This shows you understand the math represents something real!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. To find the percent growth or decay rate from an exponential function, look at the base: if it's written as (1 + r), then r is your rate. For example, (1.03)^t means 3% growth because 1.03 = 1 + 0.03. If the base is less than 1, like 0.97 = 1 - 0.03, that's a 3% decay. In the function A(t) = 1500(1.04)^t, the 1500 is the initial balance ($1500 when t = 0), and the base 1.04 means the balance is multiplied by 1.04 each year. Since 1.04 = 1 + 0.04, this represents 4% growth per year. Each year, the balance is 4% larger than the year before! Choice A is correct because it properly identifies that a base of 1.04 represents 4% growth per year. Perfect! Choice B has the growth rate wrong: a base of 1.04 means 4% growth, not 1.04%. The trick is that 1.04 = 1 + 0.04, and that 0.04 is the 4% rate. Subtract 1 from the base to get the decimal rate! For exponential functions y = a·b^x: a is what you have at time zero (plug in x = 0 and you get a), and b tells you the multiplication factor each time period. To find the percent rate: subtract 1 from b if b > 1 (like 1.05 → 0.05 = 5% growth), or subtract b from 1 if b < 1 (like 0.95 → 1 - 0.95 = 0.05 = 5% decay).

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function C = 35m + 60, the slope 35 represents the rate of $35 per month, and the y-intercept 60 represents a $60 one-time sign-up fee. So the full story is: you pay $60 upfront plus $35 for each month. Choice B is correct because it properly identifies that 60 represents the one-time sign-up fee. Perfect! Choice A confuses the slope with the y-intercept: the 60 is actually the y-intercept, which represents the starting value. It's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! For linear functions y = mx + b in context: m is always the rate (the 'per' something amount—$35 per month), and b is always the starting value (the amount when x = 0—$60 initial fee). If you can identify what's changing at a constant rate (that's m) vs what's there from the beginning (that's b), you've got it!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function C = 8n + 20, the slope 8 represents the cost increase of $8 per month, and the y-intercept 20 represents a $20 initial fee. So the full story is: you pay $20 upfront (starting fee) plus $8 for each month of service. Choice B is correct because it properly identifies that the y-intercept 20 represents the starting fee of $20 when n = 0 months. Perfect! Choice A confuses the y-intercept with the slope: the 20 is actually the y-intercept (starting fee), not the monthly rate. It's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! In context, always state the full interpretation with units: don't just say 'the y-intercept is 20'—say 'the y-intercept is $20, meaning there's a $20 starting fee before any months of service.' This shows you understand the math represents something real!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function C = 2.25m + 4.50, the slope 2.25 represents the rate of $2.25 per mile, and the y-intercept 4.50 represents the initial booking fee of $4.50 when no miles are traveled. So the full story is: you pay $4.50 upfront plus $2.25 for each mile of the ride. Choice B is correct because it properly identifies that 2.25 represents the per-mile rate increase with units and context. Choice A confuses the slope with the y-intercept: the 2.25 is actually the slope, which represents the per-mile rate, not the initial fee—it's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! For linear functions y = mx + b in context: m is always the rate (the 'per' something amount—like $2.25 per mile), and b is always the starting value (the amount when x = 0—like $4.50 booking fee); if you can identify what's changing at a constant rate (that's m) vs what's there from the beginning (that's b), you've got it!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. In a linear function like y = mx + b, the slope m represents the rate of change—how much y increases (or decreases if negative) for each one-unit increase in x—while the y-intercept b represents the starting value or initial amount when x = 0. In the function C = 3n + 12, the slope 3 represents the cost per movie ($3 per movie rented), and the y-intercept 12 represents the base fee ($12 when n = 0, before any movies are rented). So the full story is: you pay $12 as a base fee plus $3 for each movie you rent. Choice A is correct because it properly identifies that 3 represents the cost increase per movie—each additional movie costs $3. Perfect! Choice B confuses the slope with the y-intercept: the 3 is actually the rate per movie (slope), not a one-time fee. It's easy to mix these up when you're learning, but remember: in y = mx + b, m is the rate and b is the starting value! For linear functions y = mx + b in context: m is always the rate (the 'per' something amount—$5 per item, 60 miles per hour), and b is always the starting value (the amount when x = 0—$20 initial fee, 50 degrees starting temperature). In context, always state the full interpretation with units: don't just say 'the slope is 3'—say 'the slope is 3 dollars per movie, meaning each additional movie costs $3.' This shows you understand the math represents something real!

This question tests your ability to interpret the numbers in linear and exponential functions and understand what they mean in real-world contexts. To find the percent growth or decay rate from an exponential function, look at the base: if it's written as (1 + r), then r is your rate. For example, $(1.03)^t$ means 3% growth because 1.03 = 1 + 0.03. If the base is less than 1, like 0.97 = 1 - 0.03, that's a 3% decay. The base 0.9 means multiply by 0.9 each hour, and since 0.9 = 1 - 0.1, this represents a 10% decrease per hour. We subtract 0.9 from 1 to find the decay rate: 1 - 0.9 = 0.1 = 10%. Choice C is correct because it properly identifies that the percent decay rate is 10% per hour. Perfect! Choice A has the growth rate wrong: a base of 0.9 means 10% decay, not 0.9% or 9%. The trick is that 0.9 = 1 - 0.1, and that 0.1 is the 10% rate. Subtract the base from 1 to get the decimal rate! For exponential functions y = $a·b^x$: a is what you have at time zero (plug in x = 0 and you get a), and b tells you the multiplication factor each time period. To find the percent rate: subtract 1 from b if b > 1 (like 1.05 → 0.05 = 5% growth), or subtract b from 1 if b < 1 (like 0.9 → 1 - 0.9 = 0.1 = 10% decay). Quick check for exponential: if the base b = 1.03, think '1 plus 0.03, so that's 3% growth.' If b = 0.97, think '1 minus 0.03, so that's 3% decay.' The distance from 1 is the rate, and whether it's above or below 1 tells you growth or decay!