write the exponential functionSolutionThe exponential functi

write the exponential function

Solution

The exponential function is given by : y(t) = 0.75(1-0.25)^t = (0.75)(0.75)^t = (0.75)^t+1

Now we want y(t) = 0.1

So 0.1 = (0.75)^t+1

ln(0.1) = (t+1)ln(0.75)

=> ln(0.1)/ln(0.75) = t+1

=> 8.003 = t+1

=> 8.003-1= t

=> 7 = t

Approximately 7 seconds