The 10-hour decay factor for the number of mg of caffeine in Joseph's body is 0.2601.
Exponential decay is the decrease in quantity N according to:
N(t) = quantity N at time t
k = decay constant associated to physical properties of N
Substituting the values from the problem:
t = 10 hours
Then, solving for k:
Taking log on both side
Therefore, for 10-hours decay factor = 0.13467
For t = 5 hours, the decay factor is given by:
Therefore, for 5-hours decay factor =0.50999
For t = 1 hours, the decay factor is given by:
Therefore, for 1-hour decay factor =0.87400
If there are 166 mg in Joseph's body 1.38 hours after consuming the energy drink, then you could take this value as the initial value of quantity N0 Then, the quantity of caffeine in Joseph's body 2.38 hours later is just the quantity N(t) one hour later from the initial value (166 mg), then:
N(1)= 145.084 mg
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. Then graph the function.
In the exponential growth or decay function
Consider the following case of exponential growth. Complete parts a through c below.
The population of a town with an initial population of 75,000 grows at a rate of 5.5% per year.
a. Create an exponential function of the form