Writing and interpreting exponential functions

In the year 2010, a scientist determined there were 3000 of a certain type of fish in a lake. The table shows the fish population in the lake increased exponentially at a rate of 10% each year.

Based on this information, which equation can be used to predict the fish population 3 years after 2010?

• A

• B

• C

• D

Question 7

What is the equation for this problem?

• $y=500,000(1+0.05)^x$

• $y=1.05(500,000)^x$

• $y=500,000(1-0.05)^x$

• $y=500,000(0.95)^x$

What is the explicit formula for the sequence?

2, 6, 18, 54, ...

•  $a_n=-9\left(-5\right)^{n-1}$ 

•  $a_n=-10\left(-5\right)^{n-1}$ 

•  $a_n=2\left(3\right)^{n-1}$ 

•  $a_n=2\left(-3\right)^{n-1}$ 

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• $y\ =\ 5000\left(1-\frac{30}{100}\right)^t$

• $y\ =\ 5000\left(1+\frac{30}{100}\right)^t$

• $y\ =\ 30\left(1-\frac{5000}{100}\right)^t$

• $y\ =\ 30\left(1+\frac{5000}{100}\right)^t$

What is the equation that models the function below as a function of time in weeks.

You have $100 and spend $5 every week.

• f(x)=100^x+5

• f(x)=5x+100

• f(x)= -5x+100

• f(x) = 5^x

On Tuesday, 1,569 people tested positive for Covid-19 in Louisiana. The number of people who test positives grows exponentially over the next few days. The rate of growth is 1.2% per day. Write an equation that represents the number of people that test positive for Covid-19 after t days.

• $y=1569e^{.012t}$

• $y=1569e^{1.2t}$

• $y=1.2e^{^{1569t}}$

• $y=0.012e^{1569t}$

Which equation(s) can possibly represent this situation? Select ALL that apply

• y = 7800(0.92)^t

• $y=7800\left(0.92\right)^6$

• y = 1.08(7800)^t

• y = 0.92(7800)^t

• $y\ =7800\left(1-.08\right)^t$

A particular type of cell doubles in number every hour. Which function can be used to find the number of cells presents at the end of h hours if there are initially 4 of these cells?

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

• f(x)=1.03(400)^x
• f(x)=400(.97)^x
• f(x)=400(1.03)^x
• f(x)=400(0.03)^x