Question

Hello could you please help me with question number 10?

Answer 1

Exponential Model

Some phenomena can be modeled as an exponential function of the form:

`P=P_o(1+r)^t`

Where Po is the initial value, r is the rate of change, and t is the time.

If the value of P decreases in time (decaying function), then r is negative. If the value of P increases in time (growth), then r is positive.

We know an investment of Po=$4500 has been losing value (decay) at a rate of r = -2.5% = -0.025 each year.

The value of the investment when t = 5 years is:

`P=4500(1-0.025)^5`

Calculating:

`\begin{gathered} P=4500(0.975)^5 \\ P=4500\cdot0.8810957 \\ P=3964.93 \end{gathered}`

The investment will be worth $3964.93 in 5 years