# Logarithmic Functions

Suppose you deposit \$2,000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account, answer the following questions.

1.) How much money will be in the account after 3 years?
2.) How much money will be in the account after 18 years?
3.) How many years will it take for the account to contain \$2,500?
4.) How many years will it take for the account to contain \$3,000?

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1. #1 2000* 1.04^3
#3. 2000 * 1.04^x = 2500
1.04^x = 1.25
x = ln1.25/ln1.04

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2. #1
amount = 2000(1.04)^3 = ....
#2
same thing

#3.
the unknown is the time in our formula
2000(1.04)^t = 2500
1.04^t = 1.25
take log of both sides
log[ (1.04^t] = log 1.25
use rules of logs
t log 1.04 = log 1.25
t = log 1.25/log 1.04 = appr 5.7 years

#4
same thing

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