Question

The table below shows the concentration of theophylline, a common asthma drug, in the blood stream as a function of time afterinjection of a 300-mg initial dose. It is claimed that this data set is consistent with an exponential decay model C = ab' where Cisthe concentration and is the time.013579.Time (hours)Concentration (mg/l)12.010.0 7.0 5.03.52.5(a) Estimate the values of a and b, using ratios to estimate b.Enter the exact value for a. Round your answer for b to three decimal places.a =b(b) Use a calculator or computer to find the exponential regression function for concentration as a function of time.Round the answers for a and b to three decimal places.C = ab' where a = iand b = 1

Answer 1

In this problem we have an expoential function of the form

c=a(b^t)

In this problem

a is the initial value

Is the value of C when the time is equal to zero

looking at the table

For t=0

C=12

therefore

C=12(b^t)

Find the value of b

we have that

For t=1 ------> C=10

substitute

10=12(b^1)

10=12(b)

b=10/12

simplify

b=5/6

b=0.833

therefore

The equation is equal to

C=12(0.833^t)

therefore

a=12

b=0.833