For a function of , the average rate of change can be found as follows:
So, this problem asks for the Average Rate of Change of from
to
. In this way, we need to find
. As you can see above, we have the graph of
, so we can find these values. Thus, from the graph:
Therefore:
1) Since this is a Continuously Compounded operation in a 10 yrs period, then we can write out the following equation:
2) Plugging into the equation the given data and since Otto is 20 yrs old and he plans to get $4,000 in ten years, we can write out:
3) Thus the rate Otto needs is
Note that since the 0.1386 the six here is greater than 5 then we can round up to the next thousandth, in this case: 0.139. For the 0.1386 is closer to 0.139 (0.004) than to 0.138 (0.006).
Or 13.9%