Question

The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P=152.7ekt, where t represents the rear, with t=0 corresponding to 2000 . In 2008 , the population of Tallahassee was about 171,847

Use the model to predict the populations of Tallahassee (in thousands) in 2025 and 2030. (Round your answers to three decimal places.)
2025 P=
2030 P=

Answer 1

To predict the populations of Tallahassee in 2025 and 2030 using the given model, we first solve for k using the information provided. Then, we substitute the values of t into the equation to find the predicted populations.

Step-by-step explanation:

To predict the populations of Tallahassee in 2025 and 2030 using the given model, we substitute the values of t into the equation P = 152.7e^(kt). Using the information provided, we know that in 2008, t = 8 and P = 171.847. We can solve for k by substituting these values into the equation and solving for k:

171.847 = 152.7e^(k*8)

Dividing both sides by 152.7:

e^(8k) = 1.125

Taking the natural logarithm of both sides:

8k = ln(1.125)

k = ln(1.125)/8 ≈ 0.01621

Now that we have the value of k, we can use the model to predict the populations in 2025 and 2030:

For 2025, t = 25:

P = 152.7e^(0.01621*25)

P ≈ 274.03

For 2030, t = 30:

P = 152.7e^(0.01621*30)

P ≈ 291.19