# Math--Exponential Functions

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Suppose an investment of \$500 doubles in value every 15 years. How much is the investment worth after 30 years? After 45 years?

• Math--Exponential Functions -

Initial investment = \$500
Investment value after 15 years
= \$500*2
= \$1000 (doubles)

15 more years later (30), value of investment
= \$1000 * 2
= \$2000 (doubles from 15 years ago)

I will leave it to you to calculate the value of investment at 45 years from the initial investment.

Mathematically, let P = initial principal,
2P = PR^15 (R=interest rate)
R=e^(ln(2)/15)=1.047294123

Value of investment after N years,
V(N)=\$500*R^N
for N=15,
V(15)=\$500*1.047294123^15
=\$1000.00
V(30)=\$500*1.047294123^30
=\$2000.00
and so on.

• Math--Exponential Functions -

after 30 yrs the investment is worth \$2,000

after 45 yrs the investment is worth \$4,000

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