**Problem Statement:**The population of a small town is modeled by the equation $ P(t) = 6800 \cdot e^{0.14t} $ where $ t $ is measured in years. In approximately how many years will the town's population reach 19800? (Round to the nearest tenth of a year.)**Solution:**To find $ t $ when the population reaches 19800, solve the equation:1. Set $ P(t) = 19800 $.2. Substitute the given population equation: \[ 19800 = 6800 \cdot e^{0.14t} \]3. Divide both sides by 6800: \[ \frac{19800}{6800} = e^{0.14t} \]4. Simplify: \[ 2.9118 = e^{0.14t} \]5. Take the natural logarithm (ln) of both sides: \[ \ln(2.9118) = 0.14t \]6. Solve for $ t $: \[ t = \frac{\ln(2.9118)}{0.14} \]7. Calculate $ t $ and round to the nearest tenth. The answer will provide the approximate number of years required for the town's population to reach 19800.

given equation for population of small town : P(t) = 6800 e0.14t

The population of a small town is modeled by the equation P(t) 6800 e14 where t is measured in years. In approximately how many years will the town's population reach 19800? (Round to the nearest tenth of a year.) years =

The population of a small town is modeled by the equation P(t) 6800 e14 where t is measured in years. In approximately how many years will the town's population reach 19800? (Round to the nearest tenth of a year.) years =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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