Question

does the function $f(x)=0.7e^{0.64x}$ represent continuous growth, continuous decay, or neither?
○ the function represents continuous growth because $r > 0$.
○ the function represents continuous growth because $r < 0$.
○ the function represents continuous decay because $r > 0$.
○ the function represents continuous decay because $r < 0$.
○ the function represents neither because $p < 1$.
○ the function represents neither because it is not exponential.

Explanation:

Step1: Recall continuous growth/decay form

The standard continuous exponential model is $f(x) = Pe^{rx}$, where $P$ is the initial value, $r$ is the growth/decay rate.

Step2: Identify $r$ in given function

For $f(x)=0.7e^{0.64x}$, $r=0.64$, so $r>0$.

Step3: Match to growth/decay rule

When $r>0$, the function represents continuous growth.

Answer:

The function represents continuous growth because $r > 0$.