Choose the one alternative that best completes the statement or answers the question.
-In year 0, the number of female athletes participating in Summer Olympic-Type Games was 550. In year 11, about 3600 participated in the Summer Olympics in Atlanta. Assuming that and $P ( 0 ) = 500$ that the exponential model applies, find the value of k rounded to the hundredths place, and write
The function.
A) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.27 \mathrm { t } }$
B) $\mathrm { k } = 0.16 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.16 \mathrm { t } }$
C) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
D) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.19 \mathrm { t } }$

Question

Choose the one alternative that best completes the statement or answers the question.
-In year 0, the number of female athletes participating in Summer Olympic-Type Games was 550. In year 11, about 3600 participated in the Summer Olympics in Atlanta. Assuming that and $P ( 0 ) = 500$ that the exponential model applies, find the value of k rounded to the hundredths place, and write
The function. 
A) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.27 \mathrm { t } }$
B) $\mathrm { k } = 0.16 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.16 \mathrm { t } }$
C) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
D) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.19 \mathrm { t } }$

Quizplus · Accepted Answer

The exponential growth model is $P(t) = P_0e^{kt}$, where $P_0$ is the initial amount, $P(t)$ is the amount at time $t$, and $k$ is the growth rate. Given $P(0) = 500$ and $P(11) = 3600$, we can solve for $k$ by substituting these values into the model: $3600 = 500e^{11k}$. Solving for $k$ gives $k \approx 0.17$, so the correct function is $P(t) = 500e^{0.17t}$.

Choose the One Alternative That Best Completes the Statement or Answers