After x weeks of prcatice, a student can type f(x)=80(1-e^-0.3x)words a minute. How sooon will the student be able to type 60 words per minute? (Round to the nearest tenth)

f(x)=80(1-e^-0.3x) = 60

1-e^(-0.3x) = 60/80 = 3/4
e^(-0.3x)=1-3/4=1/4
e^(0.3x) = 4
Take log to base e
0.3x = ln(4)
x = ln(4)/0.3 weeks.

You meant ln1/4

e^(-0.3x)=1-3/4=1/4

=>
-0.3x = ln(1/4)
x=ln(1/4)/(-0.3)
=ln(4)/0.3
= approx. 4.6 weeks.

To find out how many weeks it will take for the student to be able to type 60 words per minute, we need to solve the equation f(x) = 60, where f(x) is given by f(x) = 80(1-e^(-0.3x)).

1. Start by substituting 60 for f(x) in the equation:
60 = 80(1-e^(-0.3x)).

2. Divide both sides of the equation by 80 to isolate the exponential term:
0.75 = 1 - e^(-0.3x).

3. Rearrange the equation to isolate the exponential term:
e^(-0.3x) = 1 - 0.75.

4. Simplify the right side of the equation:
e^(-0.3x) = 0.25.

5. Take the natural logarithm (ln) of both sides to remove the exponential:
ln(e^(-0.3x)) = ln(0.25).

6. Use the property of logarithms (ln(e^a) = a) to simplify the left side of the equation:
-0.3x = ln(0.25).

7. Divide both sides of the equation by -0.3 to solve for x:
x = ln(0.25) / -0.3.

8. Use a calculator to find the approximate value of x:
x ≈ 3.536.

Therefore, it will take approximately 3.536 weeks for the student to be able to type 60 words per minute.