Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y=12(1.05)^t. Evaluate the function when t=5. Round your answer to the nearest tenth.

Accepted Solution

Answer:Initial amount is 12Rate of growth is 5%At t = 5, y = 15.3.Step-by-step explanation:This is an exponential function. An exponential function has the form:[tex]f(x) = a_0(1+r)^t[/tex] where the original/initial amount is [tex]a_0[/tex], the growth rate is [tex]1+r[/tex] and the time is [tex]t[/tex].This means for the equation [tex]y = 12(1.05)^t[/tex]:the initial amount is 12the growth rate is 1.05 so the rate is 0.05 or 5%Substitute t = 5 into the equation to find the amount at 5.[tex]y = 12(1.05)^5\\y = 12(1.276)\\y= 15.3[/tex]