Question

Steven was given the function, f(x)=1.05^2t and asked to determine the rate of change and the type of exponential function. What is the best way for Steven to describe the function?

A. The rate of change is -1.05% and represents exponential decay.
B. The rate of change is -5% and represents exponential decay.
C. The rate of change represents 5% and represents exponential growth.
D. The rate of change is 1.05% and represents exponential growth.

Answer 1

The function f(x)=1.05^2t represents exponential growth with a rate of change of 5%.

Step-by-step explanation:

To determine the rate of change and the type of exponential function represented by the given function, f(x)=1.05^2t, we need to analyze the base of the exponential function. In this case, the base is 1.05. If the base is greater than 1, it represents exponential growth, and if it is between 0 and 1, it represents exponential decay.

Since the base, 1.05, is slightly greater than 1, it represents exponential growth. Therefore, the best way for Steven to describe the function is option C: The rate of change represents 5% and represents exponential growth.

Answer 2

`f(x)=1.05^(2t)`
The term 1.05 consists of the initial value 1 and the rate of change 0.05, (the latter being expressed as a decimal).
Therefore the correct answer choice is C.