Question

The population of Florida was about 16.05 million in 2000 and 18.81 million in 2010. Determine the average annual percent increase in population during those years and predict Florida’s population in 2025, assuming the population continues to increase at the same rate. Show your work.

16%; ≈ 23.86 million people

1.6%; ≈ 27.97 million people

16%; ≈ 656.03 million people

1.6%; ≈ 23.86 million people

Answer 1

Let r be the annual growth rate (as a decimal). With exponential growth,
(1 + r)^10 = 18.81 / 16.05.

Compute r:
r = (18.81 / 16.05)^(1/10) − 1
= exp[(1/10) ln(18.81/16.05)] − 1
≈ exp(0.01588) − 1
≈ 0.01599 ≈ 1.6%.

Predict 2025 (15 years after 2010) using P = 18.81(1 + r)^15:
P2025 ≈ 18.81 × (1.01599)^15
≈ 18.81 × 1.269
≈ 23.86 million.

Answer: 1.6% per year (approx); projected population in 2025 ≈ 23.86 million.