SOLUTION: So I need help with these exponential function problems. I have solved for the most part using Logarithms, but I still do not understand how to graph them, I need to show full solu

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: So I need help with these exponential function problems. I have solved for the most part using Logarithms, but I still do not understand how to graph them, I need to show full solu      Log On


   

Question 1155437: So I need help with these exponential function problems. I have solved for the most part using Logarithms, but I still do not understand how to graph them, I need to show full solutions so I thought if i graphed them The teacher would understand
A bicycle loses its value each month after it is purchased. It’s value as a function of time, in months, is modelled by V(m)=2200(0.98)^m. In which month after it is purchased does the bicycles worth fall below $1,500?
A 150 g sample of protactinium-233 has a half-life of 27 days. How long will it take for this sample to decay to 100 g?
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


It's not clear what help you are asking for....

The easiest way to solve problems like these is with a graphing calculator.

For the first problem, graph the functions 2200%280.98%5Ex%29 and 1500 and find their point of intersection.

graph%28400%2C400%2C-10%2C30%2C-500%2C2500%2C2200%280.98%5Ex%29%2C1500%29

Algebraically,

2200%280.98%5Ex%29+=+1500
0.98%5Ex+=+1500%2F2200+=+15%2F22
x%2Alog%28%280.98%29%29+=+log%28%2815%2F22%29%29
x+=+log%28%2815%2F22%29%29%2Flog%28%280.98%29%29 = 18.96 to 2 decimal places

ANSWER: It will take 19 months for the value to drop below $1500.

For the second problem about half lives, the formula is

y+=+A%281%2F2%29%5Ex

where x is the number of half-lives. For your problem,

150%281%2F2%29%5Ex+=+100

Again the easiest solution is with a graphing calculator.

graph%28400%2C400%2C-1%2C2%2C-50%2C200%2C150%28.5%5Ex%29%2C100%29

Algebraically,

150%281%2F2%29%5Ex+=+100
%281%2F2%29%5Ex+=+100%2F150+=+2%2F3
x%2Alog%28%281%2F2%29%29+=+log%28%282%2F3%29%29
x+=+log%28%282%2F3%29%29%2Flog%28%281%2F2%29%29 = 0.585 to 3 decimal places.

ANSWER: It will take about 0.585 half lives, or 0.585*27 = 15.8 days, for the amount to drop to 100g.