Solve.
-In 1985, the number of female athletes participating in Summer Olympic-Type Games was 450. In 1996, about 3650 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) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.29 \mathrm { t } }$
B) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
C) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.19 \mathrm { t } }$
D) $\mathrm { k } = 0.21 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.21 \mathrm { t } }$

Question

Solve.
-In 1985, the number of female athletes participating in Summer Olympic-Type Games was 450. In 1996, about 3650 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) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.29 \mathrm { t } }$
B) $\mathrm { k } = 0.17 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.17 \mathrm { t } }$
C) $\mathrm { k } = 0.19 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.19 \mathrm { t } }$
D) $\mathrm { k } = 0.21 ; \mathrm { P } ( \mathrm { t } ) = 500 \mathrm { e } ^ { 0.21 \mathrm { t } }$

Quizplus · Accepted Answer

Given $P(0) = 500$ and $P(t) = 500e^{kt}$, we use the data point from 1996, which is 11 years after 1985, and $P(11) = 3650$. Substituting these values into the equation gives $3650 = 500e^{11k}$. Solving for $k$ gives $k \approx 0.19$, making the correct function $P(t) = 500e^{0.19t}$.

Solve -In 1985, the Number of Female Athletes Participating in Summer

Solve
-In 1985, the Number of Female Athletes Participating in Summer