Question

Solve.In 1985, the number of female athletes participating in Summer Olympic-Type Games was 500. In 1996, about 3550 participated inthe Summer Olympics in Atlanta. Assuming that P(0) = 500 and that the exponential model applies, find the value of k rounded to thehundredths place, and write the function.A k = 0,18; P(t) = 500e0.181B K = 0.2; P(t) = 50000.20© K = 0.18: P(t) = 500e0.28K = 0.16; P(t) = 500e0.166

Answer 1

From the question, you can see that there is an increase in the number of population as the year increses. The exponential equation to represent this scenario is expressed as;

P(t) = P0e^kt

k is the constant of variation

P0 is the initial population

P(t) is the population after some time t

From the question;

We are given P0 =500

If in 1996, about 3550 participated in the Summer Olympics in Atlanta, this means;

at t = 11 (number of years between 1985 and 1996), P(t) = 3550

Substitute into the formula;

3550 = 500e^11k

find k;

Divide both sides by 500

3550/500 = 500e^11k/500

7.1 = e^11k

Apply ln to both sides

ln 7.1 = lne^11k

ln 7.1 = 11k

k = ln 7.1/11

k = 1.9601/11

k = 0.17819

k = 0.18

The resulting exponential equation will be;

P(t) = 500e^0.18t

The correct option is A. k = 0,18; P(t) = 500e^0.18t