Algebra 1 Question of the Day

1. The number of bacteria decreases by 10% each hour.
2. The number of bacteria increases by 1.10 bacteria each hour.
3. The culture starts with 1.10 bacteria at $t=0$ hours.
4. The number of bacteria increases by 10% each hour (multiplied by 1.10 each hour). (correct answer)

Explanation: 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!