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A quantity with an initial value of 170 decays continuously at a rate of 0.75% per day. What is the value of the quantity after 56 days, to the nearest hundredth?

User Masterwok
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1 Answer

3 votes

Answer:

A ≈ 102.56

Explanation:

The quantity decays continuously at a rate of 0.75% per day, which means that the amount of the quantity remaining after a certain number of days can be calculated using the formula:

A = A0 * e^(-rt)

where:

A0 is the initial value of the quantity

r is the decay rate (expressed as a decimal)

t is the number of days

e is the mathematical constant e (approximately equal to 2.71828)

A is the value of the quantity after t days

Substituting the given values, we get:

A = 170 * e^(-0.0075 * 56)

Using a calculator, we get:

A ≈ 102.56

Therefore, the value of the quantity after 56 days, rounded to the nearest hundredth, is approximately 102.56.

User David Pierre
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