SOLUTION: During a period of constant inflation, the value of a 215,000 property will increase according to the equation value = 215,000e^.08t where t is the time in years. A.) what will

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Question 540049: During a period of constant inflation, the value of a 215,000 property will increase according to the equation value = 215,000e^.08t where t is the time in years.
A.) what will be the property value in 12 years?
B.) How long will it take for the property to double in value?
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
A is really straightforward. Just put "12" in the formula where "t" is and solve.
x=215000%2A%28e%5E%28.08t%29%29=215000%2A%28e%5E%28.08%2A12%29%29
x=215000%2A%28e%5E.96%29=215000%2A2.611696
x=561514.74
Part B on the other hand take a little bit of algebra to solve. For starters, we're looking for how long it will take, so we will be solving the equation from your question for t, time. And the value we're looking for is double (2x) what it currently is. So we are solving the following formula for t:
2%28215000%29=215000%2A%28e%5E%28.08t%29%29
To do this, you just reverse the order of operations and start taking things away from the side with "t." First up, get rid of the 215000.
%282%28215000%29%29%2F215000=%28215000%2A%28e%5E%28.08t%29%29%29%2F215000
All the 215k's cancel out, so you're left with
2=e%5E%28.08t%29
Next up, get rid of "e." Quick refresher, "e" and "ln" cancel each other out.
ln%282%29=ln%28e%5E%28.08t%29%29=.08%28t%29%2Aln%28e%29
That leaves
ln%282%29=.08t or .08t=ln%282%29
The last step is to get rid of the .08; so divide each side by .08
.08t%2F.08=ln%282%29%2F.08
t=ln%282%29%2F.08=8.66
So it would take 8.66 years (8 years and 8 months) to double in value.