Question

Finding the initial amount and rate of change given and exponential function

Answer 1

Part A.

The initial value corresponds to the time equal to zero years, t=0. Then, by substituting this values into the given function, we get

$v(0)=637000(0.77)^0$

which gives

$\begin{gathered} v(0)=637000\times1 \\ v(0)=637000 \end{gathered}$

Thefore, the answer is: $ 637,000

Part B.

We can rewrite the given function as follows:

$v(t)=637000(1-0.23)^t$

where we can note that the decay factor is equal to 1 - 0.23. Therefore, the answer is: DECAY.

Part C.

From the last equation, we can note that the rate of decay is equal to 0.23, which corresponds to 23%. Therefore, the answer is: 23%