Question

The altitude A in feet of a plane t minutes after takeoff is approximated by the function a=7000 In(0.2t)+2000. Solve for the t in terms of A. What is a situation in which it would be easier to use your new equation rather than the orginal

Answer 1

`t=  (1)/(0.2) e^{(A-2000)/(7000)} = 5e^{(A-2000)/(7000)}`

And for this case we can use the last equation when we want the altitude and we want to know how many minutes the plane was at air after the takeoff

Explanation:

For this case we have the following function given :

`A = 7000 ln(0.2 t) +2000`

Where:

A = feet of a plane and t = minutes after takeoff

And we are interested to solve t in terms of A

We can begin subtracting 2000 in both sides of the equation and we got:

`A-2000 = 7000 ln (0.2t)`

Now we can divide both sides by 7000 and we got:

`(A-2000)/(7000) = ln(0.2 t)`

Now we can apply exponential in both sides of the equation and we got:

`e^{(A-2000)/(7000)}= 0.2 t`

And now we can divide both sides by 0.2 and we got:

`t=  (1)/(0.2) e^{(A-2000)/(7000)} = 5e^{(A-2000)/(7000)}`

And for this case we can use the last equation when we want the altitude and we want to know how many minutes the plane was at air after the takeoff