The following table shows the amount of caffeine in Alex's bloodstream at various times since he drank a cup of coffee. # of hours since he drank the coffee, t # of mg of caffeine in his bloodstream

Question

The following table shows the amount of caffeine in Alex's bloodstream at various times since he drank a cup of coffee.

# of hours since he drank the coffee,

# of mg of caffeine in his bloodstream

0

125

1

93.75

2

70.3125

3.5

45.6693

4.5

34.252

What is the 1-hour growth (or decay) factor for the number of mg of caffeine in Alex's bloodstream?

What is the 1-hour percent change for the number of mg of caffeine in Alex's bloodstream?

Define a function  that models the number of mg of caffeine in Alex's bloodstream in terms of , the number of hours since he drank the coffee. Be sure to use function notation.

Answer 1

Since you are given that this is an exponential function, first determine whether it is growth or decay by simply examining the values on the chart. The amount of caffeine in the bloodstream is decreasing each hour, so this must be a decay function.

Next, figure out by how much it's decreasing each hour. Note that in the first hour, the amount has decreased from 125 to 93.75. Calculating the percentage decrease.will give you 25%. (question 2)

Question 1 asks about the decay factor. To reduce any value by 25%, we multiply it by 0.75 (because 75% remains after we lose 25%). So 0.75 is the decay factor (1 minus rate of decay).

Finally, write this relationship as a function. Exponential functions are in the form a(b)^x , where a is the starting point, b is the growth or decay factor, and x is the input for time.

f(x)=125(.75)^x

Best wishes!