Solving Exponential Growth and Decay Applications with Logarithms

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

• 9766

• 9006

• 9765

• 5433

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

• 14327

• 4309

• 839

• 7680

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

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

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

A town doubles its size every 33 years. If the population is currently 6,000, what will the population be in 66 years?

• 12,000

• 24,000

• 198,000

• 396,000

The function y = 125(1.13)^x represents Mr. Gantz's recent investments where x is measured in years.  Which is NOT true?

• Mr. Gantz initial invested $125

• Mr. Gantz's money grows by 13% per year

• After 4 years Mr. Gantz will have about $203.81

• Mr. Gantz earns more money in year one than in year 5

Is this exponential growth or decay?

• Growth

• Decay

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

• 1,069 people

• 894 people

• 816 people

• 854 people

If you have $10, and your money doubles every year, how much money will you have in 10 years?

• $50

• $100

• $5120

• $10240

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth

• Decay