Question

5. Which situation(s) could be modeled by using an exponential function? Select all that apply 2 points) O a) a bank account balance that grows at a rate of 5% per year, compounded annually b) the cost of cell phone service that charges a base amount plus 20 cents per minute O c) a population of bacteria that doubles every 4.5 hours d) the concentration of medicine in a person's body that decays by a factor of one-third every hour

Answer 1

We have the general form as;

$\begin{gathered} V(x)=4(1.35)^x \\ \text{and it grows} \end{gathered}$

Here, we want to select the correct option that models the data in the table

Generally, for an exponential equation, the general form is given as;

$y=a(r)^x$

Where y is the value after some time x

a represents the initial value

r represents the rate of change

x is the time frame

Looking at the question, we can see that as the value of x is increasing (time) ; the value of v(x) is increasing. So what this mean is thet v(x) is increasing over time and hence, what we have is a growth.

Now, when x is 0, we have a value of v(x); that means the initial value is 4

So lastly, we need to get the rate of change r;

we can get it by substituting;

We have this as;

$\begin{gathered} 5.4=4(r)^1 \\ 5.4\text{ = 4r} \\ r\text{ = }\frac{5.4}{4} \\ r\text{ = 1.35} \end{gathered}$