Exponential Model
Some phenomena can be modeled as an exponential function of the form:
[tex]P=P_o(1+r)^t[/tex]
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:
[tex]P=4500(1-0.025)^5[/tex]
Calculating:
[tex]\begin{gathered} P=4500(0.975)^5 \\ P=4500\cdot0.8810957 \\ P=3964.93 \end{gathered}[/tex]
The investment will be worth $3964.93 in 5 years
