Geometric Series

Kevin Hart makes up a joke and tells it to his 5 closest friends on Sunday morning. Each of those friends tells his or her 5 closest friends on Monday morning, and so on.

Write an explicit formula to represent this scenario.

Kevin Hart makes up a joke and tells it to his 5 closest friends on Sunday morning. Each of those friends tells his or her 5 closest friends on Monday morning, and so on.

Assuming no duplications, how many TOTAL people will have heard the joke by the end of the day Friday?

After breaking my wrist, my doctor tells me to start using my wrist again slowly to get full range of motion back.  He suggests doing physical therapy for 12 minutes each day for the first week.  Each week thereafter, he suggests that I increase that time by 6 minutes. 

After how many weeks will it I be up to 60 minutes per day?

A culture of bacteria doubles every hour and there are 300 bacteria in the 1st hour.

Write the explicit formula.

A culture of bacteria doubles every hour and there are 300 bacteria in the 1st hour.

How many bacteria will be produced during ONLY the 24th hour?

The graph shows how the cost of a renting a limo for prom depends on the number of people.

Write the explicit formula.

The graph shows how the cost of a renting a limo for prom depends on the number of people.

Determine the cost of the limo for 12 people going to prom.

A piece of paper folded once is 0.2 millimeters thick. Each time folded, the paper becomes twice as thick. Studies have shown that you can only fold a piece of paper a maximum of 7 times.

Take out a piece of paper and try to fold it in half MORE than 7 times. Upload a picture of your best attempt!

Then write an explicit formula.

A piece of paper is 0.2 millimeters thick. When folded, the paper is twice as thick.

How thick will the paper be if it is folded on top of itself 7 times? (not total, just on the 7th fold)

"Evaluate" means to add up all the numbers. Find the sum. Your answers for #1-7 should just be one number.