Question

A 10-pound block of ice melts at a rate of 3% per hour. Find the weight of the block of ice after 1 day.

Answer 1

The weight of the block of ice after 1 day is of 4.81 pounds.

Explanation:

Equation for exponential decay:

The equation that models an amount after t hours, subject to exponential decay, is given by:

`A(t) = A(0)(1 - r)^t`

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A 10-pound block of ice melts at a rate of 3% per hour.

This means that
`A(0) = 10, r = 0.03`

So

`A(t) = A(0)(1 - r)^t`

`A(t) = 10(1 - 0.03)^t`

`A(t) = 10(0.97)^t`

Find the weight of the block of ice after 1 day.

One day has 24 hours, so this is A(24).

`A(24) = 10(0.97)^(24) = 4.81`

The weight of the block of ice after 1 day is of 4.81 pounds.