Question

You are staying at a hotel that has a hot tub. The quick forgot to make sure it was heated up. Right now the temperature is 70°. The clerk says it will get 10 percent warmer every hour. When will the temperature be at least 103°

Answer 1

This is a poorly worded problem.
The problem should state that the water temperature in degrees F increases 10% each hour, not that the water is warmer by 10%.

In any case, use exponential growth.

F = P(1 + r)^t

103 = 70(1 + 0.1)^t

Solve for t.

1.1^t = 103/70

log (1.1^t) = log (103/70)

t * log 1.1 = log (103/70)

t = (log (103/70))/(log 1.1)

t = 4.05

The temperature will be at least 103 deg in 4.05 hours.