Question

Element X is a radi

an experiment starts out with 490 grams of Element X, write a function to represent
the mass of the sample after t years, where the monthly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per month, to the nearest
hundredth of a percent.

Answer 1

Let r be the monthly rate of change of Element X, expressed as a decimal. We can then write the function to represent the mass of the sample after t years as:

m(t) = 490(1 + r)^(12t)

This function takes into account that there are 12 months in a year, so we need to raise the quantity (1 + r) to the power of 12t to account for the number of months that have passed.

To find the percentage rate of change per month, we can use the following formula:

percentage rate of change per month = r * 100

For example, if r = 0.02, then the function to represent the mass of the sample after t years would be:

m(t) = 490(1 + 0.02)^(12t)

And the percentage rate of change per month would be:

percentage rate of change per month = 0.02 * 100 = 2%

Note that the rate of change could be positive or negative depending on the decay or growth of Element X, but the formula above assumes a positive growth rate.