The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?

Options:

A. [1,10]        B. [10,20]      C. [15,25]     D. [1,30]

A. [1,10]

Step-by-step explanation:

Given

Required

Interval with the fastest rate of decay

The rate of change over [a,b] is calculated as:

So, we have:

A. [1,10]        

Calculate N(10) and N(1)

So:

B. [10,20]      

Calculate N(20) and N(10)

So:

C. [15,25]    

Calculate N(25) and N(15)

So:

D. [1,30]

Calculate N(30) and N(1)

So:

By comparing the values of the calculated rates,

-2.03 is the smallest, in other words; the fastest rate

Hence, the interval [1,10] has the fastest rate of decay

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step-by-step explanation: