Question

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Answer 1

The starting price of a hotem room is $48.00.

After 1 year, this price increases by 5.1%, meaning it's increased by a factor of 1.051 or 1 + 0.051:

$48.00 (1 + 0.051) ≈ $50.45

After another year, this price increases by another 5.1%, so the previous amount is increased by a factor of 1.051, which is equivalent to 1.051² times the initial price:

$50.45 (1 + 0.051) = $48.00 (1 + 0.051)² ≈ $53.02

After another year, another increase:

$53.02 (1 + 0.051) = $48.00 (1 + 0.051)³ ≈ $55.72

And so on. You should start to see where the given formula comes from,

$y = a(1+r)^t$

where a = $48.00 is the starting price, r = 0.051 is the rate at which the price increases, and t is number of years.

Then in 32 years, the price of the room will be

$48.00 (1 + 0.051)³² ≈ $235.79