Solve the problem.
-During 1991, 200,000 people visited Rave Amusement Park. During 1997, the number had grown to 834,000. If the number of visitors to the park obeys the law of uninhibited growth, find the exponential growth function
That models this data.
A) $f ( t ) = 634,000 e ^ { 0.248 t }$
B) $f ( t ) = 200,000 e ^ { 0.238 t }$
C) $\mathrm { f } ( \mathrm { t } ) = 634,000 \mathrm { e } ^ { 0.238 \mathrm { t } }$
D) $f ( t ) = 200,000 e ^ { 0.248 t }$

Question

Quizplus · Accepted Answer

The exponential growth function is given by $f(t) = f_0 e^{rt}$, where $f_0$ is the initial amount, $r$ is the growth rate, and $t$ is time. Since the initial number of visitors in 1991 (considered as $t = 0$) was 200,000, $f_0 = 200,000$. To find $r$, use the data from 1997, which is 6 years later ($t = 6$), and the number of visitors was 834,000. Plugging these values into the formula and solving for $r$ will confirm the correct growth rate, which matches the formula in option B.

Solve the Problem f(t)=634,000e0.248tf ( t ) = 634,000 e ^ { 0.248 t }f(t)=634,000e0.248t

Solve the Problem $f ( t ) = 634,000 e ^ { 0.248 t }$