Write the word or phrase that best completes each statement or answers the question.
-In year 0, the number of female athletes participating in Summer Olympic-Type Games was 500 . In year 11, about 3550 participated in the Summer Olympics in Atlanta. Assuming that $\mathrm { P } ( 0 ) = 500$ and that the exponential model applies, find the value of $\mathrm { k }$ rounded to the hundredths place, and write the function.
A) $\mathrm { k } = 0.16 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.16 \mathrm { t } }$
B) $\mathrm { k } = 0.2 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } 0.2 \mathrm { t }$
C) $\mathrm { k } = 0.18 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.18 \mathrm { t } }$
D) $\mathrm { k } = 0.18 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } 0.28 \mathrm { t }$

Question

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 $P(11) = 3550$, we can solve for $k$ by substituting these values into the model: $3550 = 500e^{11k}$. Solving for $k$ gives $k \approx 0.18$, so the correct function is $P(t) = 500e^{0.18t}$.

Write the Word or Phrase That Best Completes Each Statement P(0)=500\mathrm { P } ( 0 ) = 500P(0)=500

Write the Word or Phrase That Best Completes Each Statement $\mathrm { P } ( 0 ) = 500$