Question

2) The population of a small country grows according to the function P(t) = 1,300,000e0.05t, where t is measured in years. In how many years will the population grow to 2,500,000? Show answer in terms of In and as a decimal rounded to nearest tenth.​

Answer 1

Answer in terms of Ln:
`20*\text{Ln}\left((25)/(13)\right)\\\\`

Answer in decimal form: 13.1

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Work Shown:

`P(t) = 1,300,000e^(0.05t)\\\\2,500,000 = 1,300,000e^(0.05t)\\\\e^(0.05t) = (2,500,000)/(1,300,000)\\\\e^(0.05t) = (25)/(13)\\\\0.05t = \text{Ln}\left((25)/(13)\right)\\\\t = 20*\text{Ln}\left((25)/(13)\right)\\\\t \approx 13.0785293481332\\\\t \approx 13.1\\\\`