I need help please :(

Question

Suppose you drank a coffee and now have 140 mg of caffeine in your bloodstream. An average person's body will eliminate 50% of the caffeine every 2 hours. Draw and accurate graph to represent this situation for the first 12 hours and answer the questions below.

a) What is the equation of this exponential function.

b) Show how to use your graph to estimate the amount of caffeine in your bloodstream after 5 hours.

c) Show how to use your graph to estimate how long it would take until you have only 30 mg of caffeine remaining in your bloodstream.

d) Exponential function do not have x intercept. Explain why this doesn't make sense for this real-life application.

Answer 1

(a)

The Person has 140 mg of caffeine in his bloodstream initially.

The caffeine decreases by 50% for every 2 hours

Let us draw the table with the given specifications

Time t	0	2	4	6	8	10	12
Quantity of caffeine y	140	70	35	17.5	8.75	4.375	2.1875

The General Form of Decaying Exponential Function is .

Initially when t = 0 then y = 140

a = 140

Now if t = 2 hours then y = 50% of (140) = 70

b² = 2

b = √2

Exponential Function is

Graph

Draw the Co-ordinate plane

Plot the points found in the table

Connect the plotted ponts to a smooth curve

Therefore the Exponential function is .

Answer 2

(b)

Graph the function .

We can observe after 5 hours the amount of caffeine in the bloodstream is 24.7487 mg.

Answer 3

(c)

Graph the function .

We can observe that we have 30mg of caffiene in his bloddstream till  4.4447hours.

Answer 4

(d)

The exponential function is .

Where the parameter 140 is called function's  y intercept and the parameter √2 is called base of the function.

To find x intercept of any function substitute y = 0 in the function.

cannot be equated to zero.

Solutions does not exists.

Therefore exponential Functions do not have x-intercept.