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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!