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

Answer:

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

Step-by-step 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.