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storchak [24]
3 years ago
9

Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of

Element X, write a function to represent the mass of the sample after tt days, where the hourly 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 hour, to the nearest hundredth of a percent.
Mathematics
1 answer:
miss Akunina [59]3 years ago
5 0

Answer:

The function that represents the mass of the sample after t days is A(t) = 390(0.41)^t.

The percentage rate of change per hour is of -2.46%.

Step-by-step explanation:

Exponential amount of decay:

The exponential amount of decay for an amount of a substance after t days 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.

Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.

This means, respectively, that r = 0.59, A(0) = 390

So

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

A(t) = 390(1-0.59)^t

A(t) = 390(0.41)^t

The function that represents the mass of the sample after t days is A(t) = 390(0.41)^t.

Hourly rate of change:

Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So

-59%/24 = -2.46%

The percentage rate of change per hour is of -2.46%.

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