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The amount of water, w, in grams left in a mug that is left out in the open air to evaporate after t seconds is shown below.
What is the domain and range of this function?
domain:
range:
domain:
range:
domain:
range:
domain:
range:
The amount of water, w, in grams left in a mug that is left out in the open air to evaporate after t seconds is shown below.
What is the domain and range of this function?
domain:
range:
domain:
range:
domain:
range:
domain:
range:
domain:
range:
The time, t, has to be greater than or equal to 0, as we don't have negative amounts of time. There is no upper limit on t as the amount of time can go on and on (approaches infinity).
The grams of water, w, has to be greater than or equal to 0, and less than or equal to 10. Note that when we plug in t = 0, w = 10, which is the maximum value of water.
Remember that the domain tells us the values that the input, in this case t, can take on. And the range tells us the values that the output, in this case w, can take on.
Algebra I TEKS, (9) Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to:
(A) determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities
When you put a hot object into a cooler environment, the temperature of the object will change exponentially. Such as taking a cooking pan from a hot stovetop and then putting the pan into a pile of snow.
The function below shows the temperature C(t) in celcius of the pan after t minutes in the pile of snow.
Which is a correct interpretation of the function?
The pan temperature starts at 0°C and will continue to decrease exponentially as time passes
The pan temperature starts at 0°C and will continue to increase exponentially as time passes
The pan temperature starts at 40°C and will continue to increase exponentially as time passes
The pan temperature starts at 40°C and will continue to decrease exponentially as time passes
When you put a hot object into a cooler environment, the temperature of the object will change exponentially. Such as taking a cooking pan from a hot stovetop and then putting the pan into a pile of snow.
The function below shows the temperature C(t) in celcius of the pan after t minutes in the pile of snow.
Which is a correct interpretation of the function?
The pan temperature starts at 0°C and will continue to decrease exponentially as time passes
The pan temperature starts at 0°C and will continue to increase exponentially as time passes
The pan temperature starts at 40°C and will continue to increase exponentially as time passes
The pan temperature starts at 40°C and will continue to decrease exponentially as time passes
"The pan temperature starts at 40°C and will continue to decrease exponentially as time passes" is correct.
When t = 0, we see that C(t) = 40, as (1/2)^0 = 1.
The temperature will continue to decrease exponentially as 1/2 < 1, and taking the exponent of a positive fraction less than one results in ever decreasing values.
Algebra I TEKS, (9) Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to:
(B) interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems
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