Question

1. kyle invests $600 which earns 3% annual simple interest for 5 years. use a(t) = p(1 + rt) to determine how much money he will have after 5 years. interpret the rate of change in this situation. see examples 4 and 5

Explanation:

Step1: Identify the values of \(P\), \(r\), and \(t\)

Given \(P = 600\) (principal amount), \(r=0.03\) (annual interest rate, since \(3\%= 0.03\)), and \(t = 5\) (time in years).

Step2: Substitute the values into the simple - interest formula \(A(t)=P(1 + rt)\)

$$
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Step3: Calculate the value of \(A(5)\)

\(A(5)=690\)

For the rate of change:
The formula \(A(t)=P(1+rt)=P + Prt\). In the linear function \(A(t)=Prt+P\), the slope (rate of change) is \(Pr\).
Substituting \(P = 600\) and \(r = 0.03\), we get \(Pr=600\times0.03 = 18\). This means that Kyle's investment increases by \(18\) dollars per year.

Answer:

After 5 years, Kyle will have \(690\) dollars. The rate of change of \(18\) dollars per year means that Kyle's investment grows by \(18\) dollars each year.