Question

Question 6
Solve for x:
40 + 30e^-.2x= 50

Answer 1

To solve the equation 40 + 30e^(-0.2x) = 50 for x, divide both sides by 30, take the natural logarithm of both sides, and solve for x.

Step-by-step explanation:

To solve the equation 40 + 30e^(-0.2x) = 50 for x, we need to isolate the term with the exponential function. First, subtract 40 from both sides of the equation to get 30e^(-0.2x) = 10. Then, divide both sides by 30 to get e^(-0.2x) = 10/30. Taking the natural logarithm of both sides gives -0.2x = ln(10/30), and finally, divide by -0.2 to find x = ln(10/30)/-0.2 ≈ 2.41 minutes.

Answer 2

5.493

Step-by-step explanation:

Given expression

⇒

`40+ 30 e^(-.2x) =50\\30e^(-.2x) =10\\x^(-.2) =(1)/(3)`

apply Log to the base e on both sides

this calculation would requires a calculator or log table

`ln(e^(-0.2x) )=ln(1/3)\\-0.2x= -1.099\\x=5.493`