HW Exponential and Linear Word Problems Name:
1. The student enrollment of a high school was 1350 in 2008 and increases by 9% each year. What is the student enrollment in 2011 (3 years later)?
2. Laura hiked 11 miles on the first day of a two day hike. Day two she is able to hike at a rate of 3 miles per hour. How many total miles will she have hiked 6 hours into the second day?
3. In a science experiment you start out with 80 bacteria that double every hour. How many bacteria will you have in 5 hours? How many in 2.5 hours?
4. When exposed to air, about half of a colony of E. coli bacteria will die every 30 minutes. If you started out with 14,576 E. coli bacteria, how many would you have after 2 hours?
5. The Johnsons have a current checking account balance of $497. That amount is decreasing at a rate of about $11 per day for daily living costs. How much money do they have left 17 days into the month?
6. A new all-terrain vehicle (ATV) costs $1200. The value of the ATV decreases by 12% each year. How much would the ATV be worth in 4½ years?
7. A car loses roughly 18% of its value each year. Coach Rowan bought a van for his wife two and half years ago at $14,400. How much could Coach Rowan probably sell the van for today?
8. Daniel works as a volunteer in a homeless shelter and so far he has worked a total of 22 hours. He plans to continue working 4 hours a week for the rest of the summer. How many hours will he have volunteered if he works for another 13 week?
9. Suwanee had a population of 12,000 in 2005. Then the population increased by 2.5% each year for the next 7 years. What was the new population?
10. When ants are exposed to a chemical called Bifen, they have a 90% survival rate every ten minutes. If a colony have 125,000 ants is treated with Bifen, how many of those ants will still be alive in an hour and a half?
11. Walnut Grove elementary school orders 25 desks for each classroom plus an additional 30 spare desks. Find the total number of desks that they ordered if they have 21 classrooms. How much would they have ordered if they have 28 classrooms?
12. Janet bought a new 64G iPhone 5 for $399.99. Because of newer versions that will come out, the value of the iPhone will decrease at about 27% per year. How much will her new iphone be worth after years?
13. You use a credit card to make purchase a huge TV for $1500 your credit card compounds monthly at an annual interest rate of 19.5%. This credit card allows you to wait 6 months until the first payment. How much would you owe at the time of your first payment?
14. Below is a table on the back of a box for an air conditioning window unit. It shows total cost for running the unit per minute. How much would it cost to run the air conditioner for 500 minutes? You will need to find starting value and rate per minute in order to do this problem.
15. Coach Rowan is losing about 12% of his hair each year. Brown haired people start out with about 110,000 strands of hair on their head.
a. If he started losing hair at 20, how many hairs does he have at 31 years old?
b. Blonde hair people average about 140,000 strands of hair. If Coach Rowan were blonde, how many hairs would he have at 31?
16. The half-life of a drug is the amount of time it takes for half of the active elements to be eliminated from the body. The amount A (in milligrams) of 200mg of a Tylenol that remains in the bloodstream after t hours is given by. How much of the Tylenol would be in the blood after 6 hours?
17. Alan is trying to gain muscle weight by working out more. He is currently at 167 lbs and thinks he can gain 2.5 lbs a month with his workout plan. How much will he weigh if he works out for the next 18 months?
18. The half-life for caffeine is about 5.5 hours and can be modeled by the equation where I is the initial amount of caffeine ingested.
a. If you drink a 5-hour energy drink (138 mg of caffeine) before school (7:00am), how much of it will still be in your system when you go to bed at 10pm?
b. What about if you drink a Monster (240 mg of caffeine) instead?
c. What about if you were to drink two glasses of Coke (54 mg of caffeine per glass) at Frontera’s for a 7:00pm dinner and still go bed at the same time? How much caffeine would be in your system at bedtime?