In year 0 , the number of female athletes participating in Summer Olympic-Type Games was 450 . In year 11 , about 3550 participated in the Summer Olympics in Atlanta. Assuming that P(0)=500 and that the exponential model applies, find the value of k rounded to the hundredths place, and write the function.
A) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
B) $k = 0.19 ; P ( t ) = 500 e ^ { 0.29 t }$
C) $\mathrm { k } = 0.21 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.21 \mathrm { t } }$
D) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.19 \mathrm { t } }$

Question

In year 0 , the number of female athletes participating in Summer Olympic-Type Games was 450 . In year 11 , about 3550 participated in the Summer Olympics in Atlanta. Assuming that  P(0)=500  and that the exponential model applies, find the value of k rounded to the hundredths place, and write the function.
A) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
B) $k = 0.19 ; P ( t ) = 500 e ^ { 0.29 t }$
C) $\mathrm { k } = 0.21 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.21 \mathrm { t } }$
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 $P(11) = 3550$, we solve for $k$ using the equation $3550 = 500e^{11k}$. Solving for $k$ gives $k \approx 0.19$, so the correct function is $P(t) = 500e^{0.19t}$.

In Year 0 , the Number of Female Athletes Participating k=0.17;P(t)=500e0.17t\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }k=0.17;P(t)=500e0.17t

In Year 0 , the Number of Female Athletes Participating $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$