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# Exponential and reciprocal functions

1. Identify an exponential function. Give an example of this function related to the business environment.

Assignment Notes

Discussion Question 1: If we look at the formula to calculate the dollar amount of a \$1 we put into savings today, we see that it is fv = pv*((1+i)^n). The variables are fv = future value, pv = present value, i = interest rate per period, and n = number of periods. In the formula, n is an exponent. What does the exponent in this case tell us we need to do mathematically to the (1 + i) segment of the formula? Select a different interest rate (i) than your classmates who have already answered this question, as well as a different number of periods (n). How much money would you have at the end if you invested \$1 today (pv)?

2. Identify a reciprocal function. Give an example of this function in the business environment.

Assignment Notes

Discussion Question 2: While it is fun to look at what \$1 today will be in 20 years, in business we are more often concerned with the question, "If I receive \$100 in 5 years, what is that worth today?" We can find that answer by modifying the formula from DQ 1 and using the reciprocal. Simply put, the reciprocal of a number is 1 divided by the number. The reciprocal of 10 is 1/10. In the formula above, we divide both sides by ((1+i)^n). This creates a new formula where the fv is multiplied by the reciprocal of the original: fv*(1/((1+i)^n))=pv. Using the same interest rate and number of periods above, what would the value of \$100 in the future be today?

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

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