Choose the one alternative that best completes the statement or answers the question.
-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) $\mathrm { f } ( \mathrm { t } ) = 634,000 \mathrm { e } ^ { 0.248 \mathrm { t } }$
B) $f ( t ) = 200,000 e ^ { 0.238 t }$
C) $\mathrm { f } ( \mathrm { t } ) = 634,000 \mathrm { e } ^ { 0.238 \mathrm { t } }$
D) $\mathrm { f } ( \mathrm { t } ) = 200,000 \mathrm { e } ^ { 0.248 \mathrm { t } }$

Question

Quizplus · Accepted Answer

The exponential growth function is given by $f(t) = f(0)e^{kt}$, where $f(0)$ is the initial amount, $k$ is the growth rate, and $t$ is the time in years. Since the number of visitors was 200,000 in 1991 and grew to 834,000 by 1997, we use these values to solve for $k$. The correct formula that fits this growth is $f(t) = 200,000e^{0.238t}$, which indicates the initial number of visitors and the correct growth rate to match the increase from 200,000 to 834,000 over 6 years.

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