Write an exponential function to model the situation, then find the amount after the specified time.
A population of 120,000 grows 1.2% per year for 15 years.
A. y=1.012(1.2)^×;15.592
B. y=120,000(1.12)^×;785,524
C. y=120,000(1.2)^×;1,848,843
D. y=120,000(1.012)^×;143,512
The correct exponential function to model the situation would be:
D. y=120,000(1.012)^×;143,512
To find the amount after 15 years, we can substitute x = 15 into the function:
y = 120,000(1.012)^15
y ≈ 120,000 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898 × 1.218391898
y ≈ 143,511.83
Therefore, the amount after 15 years is approximately 143,512.