Warm Up

1) A population of 4000 triples in size every year. Find the population in 4 years.

2) A bacteria culture of 20 increases by a growth factor of 2 every hour. How many bacteria are there after 1 day?

HW Check 5.5

1) Year 2, the population was 40 lizards2) Year 1, the population was 20 lizards3) The 4th year4) r = 2, When using the table figure out what

you are multiplying by each time.5) 10 is the initial term6) Keep multiplying until you find the 10th term

Exponential Growth Word Problems

Exponential Growth Word Problems

1) Suppose a Zombie virus has infected 20 people at our school. The number of

zombies doubles every 30 minutes. Write an

equation that models this.

How many zombies are there after 5 hours?

3) A population of 4000 triples in size every 10 years.

What will the population be in 30 years?

4) Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have by the end of one day?

5) A Bacteria culture doubles in size every 8 hours. The culture starts at 150 cells.

How many will there be after 24 hours? After 72 hours?

6) The foundation of your house has about 1,200 termites. The number of termites quadruple every 6 hours.

How many termites will there be in 3 days?

7) Suppose your genius grandparents put $500 in an emergency savings account when you were born in case of a zombie apocalypse. The money in the account doubles every 15 years. Write a formula to describe the total investment.

How much is in the account when you are 15? 30? 45?

Drug Filtering

Assume that your kidneys can filter out 25% of a drug in your blood every 4 hours. You take one 1000-milligram dose of the drug. Fill in the table showing the amount of the drug in your blood as a function of time. The first three data points are already completed. Round each value to the nearest milligram

Time since taking the drug (hrs)

Amount of drug in your blood (mg)

0 10004 7508 562

121620242832364044485256606468

3. How many milligrams of the drug are in your blood after 2 days?

4. Will you ever completely remove the drug from your system? Explain your reasoning.

5. A blood test is able to detect the presence of the drug if there is at least 0.1 mg in your blood. How many days will it take before the test will come back negative? Explain your answer.

Recall: y = a•bx

Initial (starting) value = aGrowth or Decay Factor = bx is the variable, so we change that value based on what

we are looking for!

Remember that the growth or decay factor is related to how the quantities are changing.

Growth: Doubling = 2, Tripling = 3. Decay: Losing half = Losing a third =

Exponential Decay

When b is between 0 and 1!

Growth: b is greater than 1

If the rate of increase or decrease is a percent:

We use:1 + r for growth

or 1 – r for decay

for b in our explicit formula

Ex 1.

Suppose the depreciation of a car is 15% each year?

A) Write a function to model the cost of a $25,000 car x years from now.

B) How much is the car worth in 5 years?

Ex 2:

Your parents increase your allowance by 20% each year. Suppose your current allowance is $40.

A) Write a function to model the cost of your allowance x years from now.

B) How much is your allowance the worth in 3 years?