Question

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)

Answer 1

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.

Answer 2

You meant ln1/4

Answer 3

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.