Question

the population p, in thousands, of a small city is given by the following function, where t is time in years. answer parts a) through c). p(t)=\frac{400t}{3t^{2}+25} a) find the growth rate. the growth rate is \frac{10000 - 1200t^{2}}{(3t^{2}+25)^{2}} b) find the population after 11 yr. the population is after 11 years (round to the nearest integer as needed.)

Explanation:

Step1: Substitute t = 11 into P(t)

$P(11)=\frac{400\times11}{3\times11^{2}+25}$

Step2: Simplify the expression

$P(11)=\frac{4400}{3\times121 + 25}=\frac{4400}{363+25}=\frac{4400}{388}\approx11$

Answer:

11