The population of Collin County, which follows the exponential growth model... o

Question

The population of Collin County, which follows the exponential growth model... ot points Section 4.6-Modeling with Exponential and Logarithm Functions e population of Collin County, which follows the exponential growth model, increased from 264,036 in 1990 to 2000. Use this information for ?uestionsL5 1. Find the exponential growth rate k Round answer to 4 decimal placese in 1990 to 491,67 ?qiG7Sz?(,% 3e et..!D k-010622 2. Write the exponential growth function using k from Questionl- 3. What should the population be in 20127 Round to O decimal places. Po in 2012-5Bl (22) (0.0022)

Explanation / Answer

1. Let the exponential growth model be P = P0 ekt, where P0 is the initial population (population in 1990) k is the exponential growth rate and P is the population, t years from 1990. Here, P0 = 264036 and the population in 2000 is 491675 so that 491675=264036e10kor,e10k=491675/ 264036 = 1.862151373. Now, on taking natural logarithm of both the sides, we have 10k = ln1.862151373 = 0.621732471. Hence k = 0.0621732471 =0.0622 ( on rounding off to 4 decimal places).

2. The required exponential function is P =264036 e0.0622t,where P is the population, t years from 1990.

3. In 2012, t = 12 so that the population in 2012 would be 264036 e0.0622*12= 264036 e0.7464 = 264036*2.109392518 = 556956 (on rounding off to the nearest whole number).

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