The population of a town with a 2016 population of 66,000 grows at a rate of 2.5% per year a. Find the rate constant k and use it to devise an exponential growth function that fits the given data b. In what year will the population reach 176.000? Book a. Find the rate constant k k= (Type an exact answer) tents ccess Library Resources

Answer:  a) k= 0.025The exponential growth function in time t is given by :-[tex]P=66000e^{0.025t} [/tex],b)  In year 2033 the population will reach to 176,000.Step-by-step explanation:The exponential growth function in time t is given by :-[tex]P=P_0e^{kt} [/tex], where k is the rate of growth , [tex]P_0[/tex] is the initial population.Given : In 2016 , the initial population of town = [tex]66,000[/tex]The rate of growth per year=[tex]k=2.5\%[/tex]Which can be written as [tex]k=0.025[/tex]Let t be the number of years since 2016 to take population reach 176,000.Then , the required equation will be :-[tex]176000=66000e^{0.025t}\\\\\Rightarrow\ e^{0.025t}=\dfrac{176}{66} \\\\\Rightarrow\ e^{0.025t}=2.67[/tex]Taking log on both sides , we get[tex]0.025t=\log(2.67)\\\\\Rightarrow\ 0.025t=0.426511261365\\\\\Rightarrow\ t=17.0604504\approx17[/tex]Thus it will take 17 years since 2016 to reach population 176,000.Hence, In year 2033 the population will reach to 176,000.