In 2004, a can of soda cost $1.00 in a vending machine. If prices increase about 3% each year, in what year will the cost exceed 3$ using the exponential equation y=a(b)^x

Answer 1

An exponential equation has the following general form:

y = a·b^x

1. y = cost in year x = $3
2. a= starting cost = $1
3. b = (1 + rate) where rate is the growth or decay percent expressed in decimal form = 3% = 0.03
4. x = years

y = a·b^x

y = 1·(1+0.03)^x

y = (1.03)^x

3 = (1.03)^x We want to know x when y = $3

log(3) = log(1.03^x) To get x out of the exponent, we have to use logs. The log can be any base

log(3) = x·log(1.03) Used the property log(a^b) = b·log(a)

log(3)/log(1.03) = x

Use your calculator to get the answer.