SOLUTION: Milk costs $2.74 in 2002 if the rate of inflation continues it would cost $3.41 in 2024. What is the rate of inflation in July 2002? All I have so far to find out the equaiton i

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Milk costs $2.74 in 2002 if the rate of inflation continues it would cost $3.41 in 2024. What is the rate of inflation in July 2002? All I have so far to find out the equaiton i      Log On


   

Question 398519: Milk costs $2.74 in 2002 if the rate of inflation continues it would cost $3.41 in 2024. What is the rate of inflation in July 2002?
All I have so far to find out the equaiton is-
y=y1(b)^x-x1
3.41=2.74(b)^22 but I'm not sure if this is correct or the right way to figure it out
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3.41=2.74%28b%29%5E22
is a correct equation as long as b represents 1 plus the rate of inflation (as a decimal or fraction).

To solve for b, we start by isolating it and its exponent (by dividing both sides by 2.74:
3.41%2F2.74+=+%28b%29%5E22
Next we find the 22nd root of each side:
root%2822%2C+3.41%2F2.74%29+=+root%2822%2C+%28b%29%5E22%29
which simplifies to:
root%2822%2C+3.41%2F2.74%29+=+b
This is an exact expression for b. Since b is 1 plus the rate of inflation, the rate of inflation (as a decimal or fraction) will be:
root%2822%2C+3.41%2F2.74%29+-+1
And this means that the rate of inflation, as a percent will be:
%28root%2822%2C+3.41%2F2.74%29+-+1%29%2A100
This is probably not the desired form for the answer. You probably need to find a decimal approximation for the 22nd root of 3.41/2.74. For this we need our calculator (or a calculator computer program).

No calculator I know of has a button for 22nd roots. To find a 22nd root on the calculator we will take advantage of the fact that a 22nd root is 1/22 as an exponent:
%28%283.41%2F2.74%29%5E%281%2F22%29+-+1%29%2A100
Most calculators have a button for raising to a power. Most of the time it looks like "^". On some calculators it may look like x%5Ey or something like that.

If your calculator has buttons for parentheses then you can type the whole expression in at one time:
((3.41/2.74)^(1/22) - 1)*100
If you calculator does not have button for parentheses, then you will have to do it step by step:
  1. Divide 3.41 by 2.74 and save the answer.
  2. Divide 1 by 22 and save the answer.
  3. Use the exponentiation (raising to a power) button to raise the answer from step 1 to the answer from step 2 power.
  4. Subtract 1
  5. Multiply by 100.

Either way you should get a rate of inflation very close to 1%.

If you intended for "b" to be the actual percent of inflation, then your equation should have been:
3.41+=+2.74%2A%281%2Bb%2F100%29%5E22
where "i" is the actual percent of inflation. It's being divided by 100 because we should never do arithmetic with percents. Use the decimal or fraction version of the percent in calculations. Dividing by 100 converts a percent into a decimal or fraction.

If the equation looks like a compound interest equation then that's because it should. Compound interest and inflation problems are very similar. The main difference is that inflation can be positive, zero or negative while interest, as far as I know, is always positive.