Question

A nuclear scientist has a sample of 100mg of a radioactive material. She monitors the amount of material over a 30 hour period and obtains the data below: Hours 0 5 10 15 20 25 30 Mg 100 67.3 46.1 31.5 21.6 14.8 10.1 Rounding to 4 decimal places, use a graphing calculator to find an exponential model for the data. Then predict the amount of material remaining after 40 hours and round to two decimal places.

8.23 mg

5.16 mg

7.55 mg

4.72 mg

Answer 1

Let the exponential function that models the given data be

M=ab^t

M is the amount of radioactive material in mg left after t hours

a is the initial amount of radioactive material in mg=100

b is the growth factor for the given exponential function

t is time in hours.

Hence the equation becomes M=100b^t

The value b is obtained from the given data

When t=10, M=46.1, Put these values in the equation M=100b^t

46.1=100b¹⁰

Hence the equation becomes,

Now we have to calculate M=? when t=40

The amount of material remaining after 40 hours is 4.52 mg

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