The population of a city on the west coast has been growing

The population of a city on the west coast has been growing exponentially at the rate of 3% a year according to the model A(t) = 400,000e_0.03t, where A(t) is the population t years after 2009. If there were 400,000 residents in 2009, how long, i.e. find t, would it take for the population to reach 800,000? Choose the appropriate numerical answer. A(t) = 400,000e^(0.03*9) t = 2/0.03 t = In(2)/0.03 t = in(2/0.03) A(t) = 400.000e^(0.03*2009)

Solution

Dear Student Thank you for using Chegg !! Given Rate of growth of Population = 3% Population at any time t, A(t) = 40000*e^(0.03*t) where A(t) is the population t years afetr 2009 To find Time till population is 80000 Solution 80000 = 40000*e^(0.03*t) 2 = e^(0.03*t) Taking natural log both sides we get ln(2) = 0.03*t => t = ln(2)/0.03 Equation1 23.10490602 = t Since it is time after 2009 Year when population is 80000 is 2009+t 2032.1 Since equation 1 matches wth Optioon C , Opetion C is the correct answer Hence solved