Answered

Get expert advice and community support for your questions on IDNLearn.com. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

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

=======================================================

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]

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.