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QuestionA population of 56,117 animals decreases by 9.9%9.9\% yearly. Find the population after 8 years, rounded to the nearest whole number.

Studdy Solution

STEP 1

Assumptions1. The initial population is56,117 animals. The population decreases by9.9% each year3. We need to predict the population after8 years4. The decrease in population is compounded annually

STEP 2

The population decrease can be modeled by an exponential decay equation. This equation is given by=0×(1−r)t =0 \times (1 - r)^twhere- $$ is the final population- $0$ is the initial population- $r$ is the rate of decrease (expressed as a decimal) - $t$ is the time (in years)

STEP 3

Now, plug in the given values for the initial population, rate of decrease, and time into the equation.
=56,117×(1−9.9%)8 =56,117 \times (1 -9.9\%)^8

STEP 4

Convert the percentage to a decimal value.
9.9%=0.0999.9\% =0.099=56,117×(1−0.099)8 =56,117 \times (1 -0.099)^8

STEP 5

Calculate the value inside the parentheses.
1−0.099=0.9011 -0.099 =0.901=56,117×(0.901)8 =56,117 \times (0.901)^8

STEP 6

Calculate the value of the exponent.
(0.901)8≈0.4309(0.901)^8 \approx0.4309=56,117×0.4309 =56,117 \times0.4309

STEP 7

Calculate the final population.
=56,117×0.4309≈24,172.5 =56,117 \times0.4309 \approx24,172.5Since we cannot have a fraction of an animal, we round to the nearest whole number.
≈24,173 \approx24,173After years, the population is predicted to be approximately24,173 animals.

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