Question

A sample of a substance with an initial mass of 5040 grams is decaying at a rate of 32% per hour. Create a function that can be used to find y, the mass of the substance in grams remaining after x hours.

Answer 1

To calculate the mass remaining after x hours for a substance decaying at a rate of 32% per hour, use the exponential decay function y = 5040(1 - 0.32)^x, where 5040 is the initial mass in grams.

Step-by-step explanation:

To create a function that finds y, the mass of the substance remaining after x hours, when it is decaying at a rate of 32% per hour, we can use the exponential decay formula:

y = P(1 - r)^t

Where:

• P is the initial mass of the substance,
• r is the rate of decay as a decimal,
• t is the time in hours.

In this case, P is 5040 grams, r is 0.32 (since 32% as a decimal is 0.32), and t will represent the variable x for hours.

Therefore, the function will be:

y = 5040(1 - 0.32)^x

This function can be used to calculate the remaining mass of the substance after any given number of hours.