Question

Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his investment after x years:

f(x) = 300(1.02)^x

What was the average rate of change of the value of Jack's investment from the third year to the fifth year?

6.43 dollars per year

8.24 dollars per year

12.86 dollars per year

14.26 dollars per year

Answer 1

Here the average rate of change is \[avrc=\frac{ f(x _{2})-f(x _{1}) }{ x _{2}-x _{1} }\]

Answer 2

where x_1 is the starting time of the time interval and x_2 is the end time. Evaluate your function f(x) at these two values. then substitute the results into the above formula. Note that this formula is much like that for calculating the slope of a secant line.

Answer 3

How would you do that?

Answer 4

What are the two time values (x-values)? Once you have them, subtract the smaller from the larger to obtain the denominator of the "avrc" function I gave you earlier.
Now evaluate the given function f(x)=300(1.02)^x at each of these two time values.
Find \[f(x _{2})-f(x _{1})\]

Answer 5

Then evaluate the entire "avrc" defined above. Be certain to supply the correct units of measurement.