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population in thousands 400 350 300 250 200 150 100 50 9 In The population of a fast-growing city in Texas can be modeled with the equation p(t) = 82. e(0.078t). The population of a fast-growing city in Tennessee can be modeled with q(t) = 132. e(0.047t). both equations, t represents years since 2016 and the population is measured in thousands. The graphs representing the two functions are shown. The point where the two graphs intersect has a y- coordinate of about 271.7. p time in years since 2016 1. What does the intersection mean in this situation? 2. Find the x-coordinate of the intersection point by solving each equation. Show your reasoning. a. p(t) = 271.7 b. q(t) = 271.7 3. Explain why we can find out the t value at the intersection of the two graphs by solving

population in thousands 400 350 300 250 200 150 100 50 9 In The population of a fast-growing city in Texas can be modeled with the equation p(t) = 82. e(0.078t). The population of a fast-growing city in Tennessee can be modeled with q(t) = 132. e(0.047t). both equations, t represents years since 2016 and the population is measured in thousands. The graphs representing the two functions are shown. The point where the two graphs intersect has a y- coordinate of about 271.7. p time in years since 2016 1. What does the intersection mean in this situation? 2. Find the x-coordinate of the intersection point by solving each equation. Show your reasoning. a. p(t) = 271.7 b. q(t) = 271.7 3. Explain why we can find out the t value at the intersection of the two graphs by solving

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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population in thousands 400 350 300 250 200 150 100 50 9 The population of a fast-growing city in Texas can be modeled with the equation p(t) = 82. e(0.078t). The population of a fast-growing city in Tennessee can be modeled with g(t) = 132. e(0.047t). In both equations, t represents years since 2016 and the population is measured in thousands. The graphs representing the two functions are shown. The point where the two graphs intersect has a y- coordinate of about 271.7. Р time in years since 2016 1. What does the intersection mean in this situation? 2. Find the x-coordinate of the intersection point by solving each equation. Show your reasoning. a. p(t) = 271.7 b.q(t) = 271.7 3. Explain why we can find out the t value at the intersection of the two graphs by solving p(t) = g(t).
Transcribed Image Text:population in thousands 400 350 300 250 200 150 100 50 9 The population of a fast-growing city in Texas can be modeled with the equation p(t) = 82. e(0.078t). The population of a fast-growing city in Tennessee can be modeled with g(t) = 132. e(0.047t). In both equations, t represents years since 2016 and the population is measured in thousands. The graphs representing the two functions are shown. The point where the two graphs intersect has a y- coordinate of about 271.7. Р time in years since 2016 1. What does the intersection mean in this situation? 2. Find the x-coordinate of the intersection point by solving each equation. Show your reasoning. a. p(t) = 271.7 b.q(t) = 271.7 3. Explain why we can find out the t value at the intersection of the two graphs by solving p(t) = g(t).
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