Question

Does each function describe exponential growth or decay?

Answer 1

Answer: Only first two are exponential growth function and last three functions are exponential decay functions.

Step-by-step explanation: We need to describe exponential growth or decay for the given functions.

The standard exponential function equation is

$y=a(b)^x$.

Where a is the initial value and b is the growth factor.

Note: If value of b > 1, it would be an exponential growth and if b < 1, it would be an exponential decay.

Let us check them one by one.

$y=(1.008^{1/12}})^{12t}$ => $y=(1.008^})^{1/12\times{12t} }$

=> $y= (1.008)^t$.

Value of b is 1.008 > 1, therefor it's an exponential growth function.

y=250(1+0.004)^t, also have b>1 therefor it's an exponential growth function.

All other functions has b values less than 1, therefore only first two are exponential growth function and last three functions are exponential decay functions.