Question 1065837: An investment is worth $3118 in 1993. By 1998 it has grown to $3748. Let y be the value of the investment in the year x, where x=0 represents 1993. Write a linear equation that models the value of the investment in the year x.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 3798=3118(1+r)^n
This is the formula for annual rate of increase over n years.
Here, n=5
3798=3118(1+r)^5
1.2181 (don't round in calculations, however)=(1+r)^5
logs of both sides
log (1.2181)=5 log (1+r)
divide by 5 both sides
10 to the power on both sides
1.0402=1+r
subtract 1
r=0.0402 or 4%.
check
1.04^5=1.2167
3118*1.2167=3794, which is the same given the rounding.
I could expand (1+r)^5, bu that is not linear but a 5th power equation.
If this is not what is desired, please resubmit. The above equation is not linear, but accumulation of interest is not linear.
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