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Review . You deposit $1500 that pays 5%. Find the balance over 5 years. A business had a $5000 profit in 1990. Then the profit increased 15% over 10yrs. Write an exponential growth model over the 10yr. Use the model to find profit. 8.6 Exponential decay. Notes.

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Review

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  1. Review • You deposit $1500 that pays 5%. Find the balance over 5 years. A business had a $5000 profit in 1990. Then the profit increased 15% over 10yrs. Write an exponential growth model over the 10yr. Use the model to find profit.

  2. 8.6 Exponential decay

  3. Notes Exponential decay: quantity decreases by same percent over time. • Model • Y = C(1 – r)t • C = initial amount • R = rate of decay (%) • T = time • (1 – r ) is decay factor • 1 > (1- r) > 0 (deay)

  4. Find the value after depreciation –t/st • You buy a car for $15,000. It depreciates 23% per year. Find the value of the car given the year. • 1y • 3yrs • 5yrs • 8yrs

  5. Classify as exponential growth or decay. Identify growth/decay factor -t • Y = 16(1.25)t • Y = 10(

  6. Classify as exponential growth or decay. Identify growth/decay factor -t • Y = 4(0.94)t • Y = 32(0.75)t • Y = 800( • Y = 20(1.05)t

  7. Write a decay model -t • From 1982 to 1997, the purchasing power of a dollar decreased by 3.5% per year. Using 1982, as the base for comparison, what was the purchasing power in 1997? • 1. Write a decay model. • 2. Estimate the purchasing power over the time.

  8. Write a decay model -st • You bought a car for $18,000. The value of the car will be less each year because of depreciation. The car depreciates at the rate of 12% a year. • 1. Write a decay model. • 2. Estimate the value of the car after 8yrs.

  9. Complete the table. Classify as growth or decay. Id the growth or decay factor. Id the percent of increase or decrease percent. Then graph - t • Y = 30(1.2)x

  10. Complete the table. Classify as growth or decay. Id the growth or decay factor. Id the percent of increase or decrease percent. Then graph - st • Y = 2(0.25)x

  11. Word Problem - st • Between 1985 and 2000, the population of a city decreased by approximately 3% each year. In 1985 there were 450,000 people. What was the population in 2000?

  12. Word Problem • Between 1990 and 2000, the profits of a business decreased approximately 0.7% each year. In 1990 the business’s profit was $1.4 million. Write an exponential decay model showing the profit P in terms of year t. What was the profit in 2000?

  13. Wrap up • Questions/Comments • Hw: text pg. 488, #’s: 1,2, 10-22, 27,28, 30

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