Thread: how to find time in exponential equation.

I'm trying to solve these two problems that both involve solving for t, and I have been trying to figure it out for hours and simply have no idea what to do. Can someone please guide me through how to set up these two problems?

Industrial psychologist study employee training programs to assess the effectiveness of the instruction. In one study, the percent score P on a test for a person who has completed t hours of training was given by P= 100/1+30e^-.088t. How many hours of training are necessary to achieve a 70% on the test?

and

Assuming that air resistance is proportional to the velocity of a falling object, the velocity (in feet per second) of an object t seconds after it has been dropped is given by V=82(1-e^-.39t). When will the velocity be 70 feet per second? Show all of your work or explain how you came up with your solution.

Any help/guidance would be so much appreciated!! Thanks so much.

Originally Posted by kmproffitt2010

I'm trying to solve these two problems that both involve solving for t, and I have been trying to figure it out for hours and simply have no idea what to do. Can someone please guide me through how to set up these two problems?

Industrial psychologist study employee training programs to assess the effectiveness of the instruction. In one study, the percent score P on a test for a person who has completed t hours of training was given by P= 100/1+30e^-.088t. How many hours of training are necessary to achieve a 70% on the test?

I think you mean P= 100/(1+ 30e^(-0.88t)) which is not what you wrote. You want to solve the equation .7= 100/(1+ 30e^(-0.88t)) That is the same as (1+ 30e^(-0.88t))/100= .70 which is the same as 1+ 30e^(-0.88t)= 70. Can you finish that?

and

Assuming that air resistance is proportional to the velocity of a falling object, the velocity (in feet per second) of an object t seconds after it has been dropped is given by V=82(1-e^-.39t). When will the velocity be 70 feet per second? Show all of your work or explain how you came up with your solution.

Any help/guidance would be so much appreciated!! Thanks so much.

So you want to solve 82(1- e^(-.39t))= 70. Divide both sides by 82 to get
1- e^(-.39t)= 70/82= 35/41. Subtract 1 from both sides: -e^(-.39t)= 35/41- 1= (35- 41)/41= -6/41. Multiply both sides by -1 to get e^(-.39t)= 6/41. Can you finish that?

thanks so much!! i finished the second problem, but i'm still not sure how to solve for t in the first one.

Is it:

? The notation is extremely unclear.

yes, but the number 30 is the coefficient of e.