Write an equation and solve each problem



Write an equation and solve each problem.

EXPONENTIAL GROWTH

1. A population of 46 animals is growing at a rate of 25% per year. How many animals will there be after 7 years?

2. If you have 200 bacteria per square foot and they double every 6 hours, how many bacteria will you have after 18 hours? 2 days?

3. Since 1990, the population of Virginia has grown at an average annual rate of about 1%. In 1990, the population was about 6,284,000.

a. Write an equation to model the population growth in Virginia since 1990.

b. Suppose this rate of growth continues. Predict Virginia’s population in 2010.

EXPONENTIAL DECAY

4. At sea level the barometric pressure is 29.92 in. of mercury. For each mile above sea level, the barometric pressure decreases 18%. Find the barometric pressure 3 miles above sea level.

5. The real estate market was depressed in many cities in the early 1990’s. Many people saw the value of their homes decrease. If a home was worth $150,000 in 1990 and the housing market in that area decreased at a constant rate of 5% per year, what was the value in 1997?

6. The half-life of iodine-124 is 4 days. A technician measures a 40-mCi sample of iodine-124.

a. How many half-lives of iodine-124 occur in 16 days?

b. How much iodine-124 is in the sample 16 days after the technician measures the original sample?

7. The value of a new car decreases exponentially. Suppose your mother buys a new car for $22,000. The value of the car decreases by 20% each year.

a. What is the initial price of the car? The decay factor?

b. Write an equation to model the value of the car x years after she buys it.

c. Find the value of the car after 6 years.

8. Write an exponential function to model the situation. A population of 3,000,000 decreases 1.5% annually. Find the population after 10 years.

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