Question

The function f(t) = 720(1.0095)^(t/7) represents the change in a quantity over t days. What does the constant 1.0095 reveal about the rate of change of the quantity?

a) The function is linear at a rate of 1.0095% every 7 days.
b) The function is exponential at a rate of 1.0095% every 7 days.
c) The function is linear at a rate of 7% every 1.0095 days.
d) The function is exponential at a rate of 7% every 1.0095 days.

Answer 1

The constant 1.0095 in the exponential function indicates that the quantity it represents increases by 0.95% every 7 days, which defines an exponential rate of change.

Step-by-step explanation:

The constant 1.0095 in the function f(t) = 720(1.0095)^(t/7) reveals that the quantity changes at an exponential rate. Specifically, the base of the exponential function, 1.0095, indicates that the quantity increases by 0.95% every 7 days, as the base is close to 1.

If the function were linear, the rate of change would be constant and the function would not have an exponent on the variable t. In contrast, exponential growth means the rate of change is proportional to the value of the function itself, leading to a quicker increase over time. Therefore, the correct answer is (b) The function is exponential at a rate of 1.0095% every 7 days.