Exponential Functions Extra Practice for Test

A certain strain of bacterium can split into three cells every hour. If you begin with two cells, you will have _____ bacteria cells after one day. The exponential function to represent this situation is _____ .

A car valued at $20,000 depreciates at the rate of 12.5% per year. Write the equation then find the value of the car after 3 years is _____ . Round to the nearest hundreth.

In 2000, there were 150 internet users in the small town of Maplewood. The number of users increased by 60% per year after 2000. The exponential function to represent this situation is _____, and the number of internet users in 2009 is _____. Round to the nearest hundreth.

Answer explanation

The exponential function is y=150(1.6)^x, where x is the number of years since 2000. For 2009, x=9, so y=150(1.6)^9, which calculates to approximately 10307.92. Thus, the correct answers are the function and the user count.

You are considering buying a house and taking out a $200,000 home loan to pay for it. The APR is 3.5%. If the loan is a 20-year loan. Write the exponential function to represent this situation then calculate how much money you will pay over the original price. Round to the nearest hundreth.

Answer explanation

The exponential function for the loan is y = 200000(1 + 0.035)^x. Over 20 years, the total payment is approximately $397,957.77. Subtracting the original price ($200,000) gives $197,957.77, which is the amount paid over the original price.

The local animal shelter is collecting donations for cat food. On average, they receive 8 cans every 3 weeks. Is there a common ratio?

• Yes, there is a common ratio.

• No, there is no common ratio.

Answer explanation

The average of 8 cans every 3 weeks does not establish a consistent ratio over time, as it does not indicate a fixed pattern of increase or decrease. Therefore, there is no common ratio.

Consider the following table showing the number of bacteria in a petri dish over time: Does this table represent an exponential function?

• Yes, there is a common ratio.

• No, there is no common ratio.

Answer explanation

Yes, the table represents an exponential function because the number of bacteria increases by a common ratio over equal time intervals, indicating exponential growth.

Choose the answer that identifies ALL of the tables, graphs, and equations that represent exponential functions.

• b,g,h,n,q

• b,g,i,m,q

• b,d,h,n.q

• b,e,h,n.q

Answer explanation

The correct choice is b,g,h,n,q, as these options include all tables, graphs, and equations that exhibit exponential growth or decay, which is characteristic of exponential functions.

A biologist is studying the growth of a certain bacteria population in a lab. The biologist records the number of bacteria at different times and obtains the following data.Using the data provided, write the exponential regression equation that models the growth of the bacteria population over time.

Answer explanation

The exponential regression equation for the bacteria population is given as y = 49.98732(1.60051)^x. This equation models the growth accurately, making it the correct choice.

A certain species of plant grows in such a way that the number of leaves doubles every week. Initially the plant has 3 leaves.

1. Write the explicit formula for the number of leaves after (n) weeks.

2. Using the formula, find the number of leaves after 12 weeks.

Write the explicit formula for the (n)-th term of the geometric sequence where the first term is 32 and the common ratio is 1/2 . Then find the 18th term of the sequence.