all exponential functions can be written in many forms. write the function f(t)=64000(2)^(t/5) in the form…

all exponential functions can be written in many forms. write the function f(t)=64000(2)^(t/5) in the form f(t)=ae^(kt). round all coefficients to four decimal places. answer attempt 1 out of 2 f(t)= e^ t

all exponential functions can be written in many forms. write the function f(t)=64000(2)^(t/5) in the form f(t)=ae^(kt). round all coefficients to four decimal places. answer attempt 1 out of 2 f(t)= e^ t

Answer

Explanation:

Step1: Recall the property $a^x = e^{x\ln(a)}$

We know that $2^{\frac{t}{15}}=e^{\frac{t}{15}\ln(2)}$.

Step2: Rewrite the original function

The original function $f(t)=64000(2)^{\frac{t}{15}}$ can be rewritten as $f(t)=64000e^{\frac{\ln(2)}{15}t}$.

Step3: Calculate the coefficients

First, $\ln(2)\approx0.693147$. Then $\frac{\ln(2)}{15}\approx\frac{0.693147}{15}\approx0.0462$. And $a = 64000.0000$.

Answer:

$f(t)=64000.0000e^{0.0462t}$