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Suppose the population of a town is 8,200 and is growing 3% each year. Write an equation to model the population growth. Predict the population after 3 years.

Verified Answer :

Aliwohaish12

P=8200(1.03)t

P is the population after t years.
t=3
P=8200(1.03)3=8960.3614=8960

SociometricStar

Answer:

  • The exponential model is given by \(Q=8200(1.03)^t\)
  • The population after 3 years is given by 8960

Step-by-step explanation:

The exponential model is given by

\(Q=A_0(1+r)^t\)

Here, Q = final population, Q_0 = initial population, r = growth/decay rate, t = time

Now, we have been given

\(Q_0=8200,r=3\%=0.03\)

On substituting these values, the model is given by

\(Q=8200(1+0.03)^t\\Q=8200(1.03)^t\)

Now, the population after 3 years is given by

\(Q=8200(1.03)^3\approx 8960\)


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