Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:

In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus,
. We use this to find k.







Then

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So


The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
The y-intercept is 2 and the Slope is 2/4 but if you simplify that, it will be 1/2.
It's increased by 10
<span>453,463,473,483...
next number would be 493</span>
Answer:
<h2>
4773 peoples.</h2>
Step-by-step explanation:
Given the number of people d, in thousands applying for medical benefits per week in a particular city c modeled by the equation d(t)=2.5 sin(0.76t+0.3)+3.8 where t is the time in years, the maximum number of people tat will apply will occur at d(t)/dt = 0
Differentiating the function given with respect to t, we will have;

First we need to know that differential of any constant is zero.

If
then;

To know the maximum number of people in thousands that apply for benefits per year in the city, we wil substitute the value of t = 29.75 into the modeled equation

Since d is in thousands, the maximum number of people in thousands will be 4.7732*1000 = 4773.2 which is approximately 4773 peoples.