I'm having trouble with these problems, can you check if they are right ? **Lab Module 4 - Exponential Growth in Collin County****Population Increase Overview:**The population of Collin County, which follows an exponential growth model, increased from 491,675 in the year 2000 to 782,341 in 2010.---**a. Exponential Growth Rate Calculation:**To find the exponential growth rate $ k $, use the exact value of the growth:- **Population Growth Formula:** \[ P(t) = P_0 e^{kt} \] - $ P_0 = 491,675 $ - $ P(10) = 782,341 $- **Calculation:** \[ 782,341 = 491,675 e^{10k} \] \[ \frac{782,341}{491,675} = e^{10k} \] \[ \ln\left(\frac{782,341}{491,675}\right) = 10k \]**Growth Rate $ k $:** \[k = \frac{\ln\left(\frac{782,341}{491,675}\right)}{10}\]---**b. Exponential Growth Function:**Using the growth rate from part a, the function is:\[P(t) = 491,675 e^{\left(\frac{\ln\left(\frac{782,341}{491,675}\right)}{10}\right)t}\]---**c. Projected Population in 2016:**- Time $ t = 2016 - 2000 = 16 $ years- Function for 2016: \[ P(16) = 491,675 e^{\left(\frac{\ln\left( \frac{782,341}{491,675} \right)}{10}\right) \cdot 16} \]**Approximate Population in 2016:** 1,033,777 people---**d. Time to Reach Population of 999,999:**- Set equation: \[ 999,999 = 491,675 e^{\left(\frac{\ln\left(\frac{782,341}{491,675}\right)}{10}\right)t} \]- Solve for $ t $: \[ \

exponential growth model P = P0ektP = population at time t P0 = initial population k = growth rate

The population of Collin County, which follows the exponential growth model, increased from 10 491,675 in 2000 to 782,341 in 2010. is ons a. Find the exponential growth rate, k. Don't round, instead use the exact value of the growth rate. Plt) Poext < population of In 782341 491675) Po 491,475 2 P(10) = 782,341 3 growth formula Sewvort & alls Inece 10k 782,341-491.675€! 491,075 249 1782341 491675 491,675 782341 66782341 491675 YDS 491475 elok in 782341: Inelok 49167hort teadlast menpillim to tedmun seya 10 -In work hela nispe bojotinim b. Write the exponential growth function. Use the exact growth rate found in a. in -/10 t P(+) 1/7 491(75 - 10K 10

The population of Collin County, which follows the exponential growth model, increased from 10 491,675 in 2000 to 782,341 in 2010. is ons a. Find the exponential growth rate, k. Don't round, instead use the exact value of the growth rate. Plt) Poext < population of In 782341 491675) Po 491,475 2 P(10) = 782,341 3 growth formula Sewvort & alls Inece 10k 782,341-491.675€! 491,075 249 1782341 491675 491,675 782341 66782341 491675 YDS 491475 elok in 782341: Inelok 49167hort teadlast menpillim to tedmun seya 10 -In work hela nispe bojotinim b. Write the exponential growth function. Use the exact growth rate found in a. in -/10 t P(+) 1/7 491(75 - 10K 10

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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