The population of a fast-growing city in Texas can be modeled with the equation p (t) = 82 - e(0.0782). The population of a fast-growing city in Tennessee can be modeled with q (t) = 132 - e(0.047). 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. 400 350 300 250 E 200 150 100 50 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 pít)=glt). population in thousands

The population of a fast-growing city in Texas can be modeled with the equation p (t) = 82 - e(0.0782). The population of a fast-growing city in Tennessee can be modeled with q (t) = 132 - e(0.047). 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. 400 350 300 250 E 200 150 100 50 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 pít)=glt). population in thousands

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The population of a fast-growing city in Texas can be modeled with the equation p (t) = 82 - e(0.0782). The population
of a fast-growing city in Tennessee can be modeled with q (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.
400
350
300
250
E 200
150
100
50
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)=q(t).
population in thousands

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