Answered

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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.​

Sagot :

Answer in terms of Ln:   [tex]20*\text{Ln}\left(\frac{25}{13}\right)\\\\[/tex]

Answer in decimal form:   13.1

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Work Shown:

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

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