Question

Suppose a house that costs $270,000 appreciates by 5% each year.

In about how many years will the house be worth $350,000? Use the equation 350 = (270)(1.05)x and round the value of x to the nearest year.

7
6
5
4

Answer 1

Please use " ^ " to indicate exponentiaton: Use the equation

350 = (270)(1.05)^x.
Take the log of both sides:

log 350 = log 270 + x*log 1.05.

Subtr. log 270 from both sides:

log 350 - log 270 = x*log 1.05
log 350 - log 270
Sove for x: x = -------------------------
log 1.05
2.544- 2.431
Evaluate this using a calculator. x = ------------------
0.0212

x is then approx. 5.33, or 5 1/3 years.