The population P of a state (in millions) x years after 2000 can be modeled by P

Question

The population P of a state (in millions) x years after 2000 can be modeled by P- 38 e 0013*. (a) Use properties of logarithms to solve this equation for» (b) Use the equation found in part (a) to find x when P 43. Interpret the answer. (a) Choose the correct answer below 38 0.013 0.013 1 P In OD. x-38 In 0.01338 0.013 (b) When P- 43, x is approximately (Type an integer or decimal rounded to the nearest tenth as needed.) Interpret the preceding result. Round up to the nearest year. Choose the correct answer below O A. The population is expected to reach 43 million during 2011 O B. The population is expected to increase by 43 million during 2011. ° C. The population is expected to reach 43 million during 2010. D. The population is expected to increase by 43 million during 2010

Explanation / Answer

a) P = 38e0.013x

or, P/38 = e0.013x

or, ln(P/38) = 0.013x

or, x = (1/0.013)ln(P/38)

Option - C is correct.

b) For P = 43

X = (1/0.013)ln(43/38)

   = 9.5 = 10

Option - C is correct.

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