The initial population of a town is 4400, and it grows with a doubling time of 10 years. What will the population be in 12 years? What will the population be in 12 years?

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Answer 1 · 2018-05-01T04:47:40

population in #12# years #~~ 10,108# people

Given: #P_o = 4400#; #10# years to double the population

Population equation: #P = P_o e^(kt)#, where k = constant;
#" "t = # number of years

Find #k# from the doubling information:

#4400 *2 = 8800#

#8800 = 4400 e^(k*10)#

#8800/4400 = 2 = e^(k*10)#

Use the logarithmic property: #" "ln e^x = x#

#ln 2 = ln e^(k*10)#

#ln 2 = k*10#

#k = (ln 2)/10#

#P = 4400 e^( (ln 2)/10t)#

Solve for the population after 12 years:

#P = 4400 e^( (ln 2)/10*12) = 4400 e^(1.2 ln2) ~~10, 108#

The initial population of a town is 4400​, and it grows with a doubling time of 10 years. What will the population be in 12 ​years? What will the population be in 12 ​years?