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 11340 after 11 years. (round to the nearest integer as needed.) c) find the growth rate at t = 11 yr. the growth rate at t = 11 yr is residents/yr (round to the nearest integer as needed.)

Explanation:

Step1: Recall given growth - rate formula

The growth - rate formula is $\frac{10000 - 1200t^{2}}{(3t^{2}+25)^{2}}$.

Step2: Substitute $t = 11$

Substitute $t = 11$ into the formula: $\frac{10000-1200\times11^{2}}{(3\times11^{2}+25)^{2}}$.

Step3: Calculate numerator

$10000-1200\times121=10000 - 145200=- 135200$.

Step4: Calculate denominator

$(3\times121 + 25)^{2}=(363+25)^{2}=388^{2}=150544$.

Step5: Calculate the result

$\frac{-135200}{150544}\approx - 1$.

Answer:

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