Question

the value of an investment of $3,500 over t years at 4.5% interest is represented by the expression 3500(1.045)^t. which kind of expression is 3500(1.045)^t? linear quadratic exponential decay exponential growth

Explanation:

Step1: Identify expression form

The given expression is $3500(1.045)^t$, which matches the exponential form $A(t)=a(b)^t$, where $a$ is the initial value, $b$ is the growth/decay factor, and $t$ is time.

Step2: Check growth/decay factor

For exponential models, if $b>1$, it is growth; if $01$.

Step3: Eliminate other options

Linear expressions have the form $mt+b$, quadratic have $at^2+bt+c$, so these do not match. Since $b>1$, it is not decay.

Answer:

exponential growth