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Exponential Growth and Decay Practice

Practice 1

Complete the table to determine the balance A for an investment of $15,000 at an interest rate of 8% for 25 years compounded n times a year.

n 1 2 4 12 365 Continuously
A            

Answer:
n 1 2 4 12 365 Continuously
A 102,727.13 106,600.25 108,669.69 110,102.64 110,811.55 110,835.84

When you have completed the table, look at the difference 25 years has made to the amount of money invested.

Look at the difference it makes when we change the number of times a year the interest was compounded.

Practice 2

Five hundred grams of Plutonium is stored in a container. The decay rate for Plutonium is 0.012% per year. How much Plutonium is left after 1000 years?

Identify the following:

  • Initial amount:______(Fill in the blank) grams
  • Decay factor:______(Fill in the blank) %
  • Time:______(Fill in the blank) years

    • Write a model where P = the population after 10 years using the formula y equals a. b to the xth power
    ______(Fill in the blank)
  • P = ______(Fill in the blank)(1 −______(Fill in the blank))
  • P = ______(Fill in the blank) grams

Answer:

  • Initial amount: 500 grams
  • Decay factor: 0.012% = 0.00012
  • Time: 1000 years

    • Write a model where P = the population after 10 years using the formula y equals a. b to the xth power
    1000
  • P = 500 (1 − 0.00012)
  • P = 443.457 grams

Practice 3, Part One

In 2000, the tuition to attend a state university was $5,000. The average increase per year since has been 6.2%. How long will it take for tuition to double?

Identify the following:

  • Initial amount: $______(Fill in the blank)
  • Growth factor:______(Fill in the blank) %
  • Amount after it doubles: $______(Fill in the blank)

    • Write a model for the tuition using the formula y equals a. b to the xth power
  • ______(Fill in the blank) = ______(Fill in the blank) (1 + ______(Fill in the blank))t
  • Divide both sides by 5000: ______(Fill in the blank) = (1 + 0.062)t
  • Change to logarithm form.
  • log ______(Fill in the blank)  ______(Fill in the blank) = ______(Fill in the blank)

Answer:

  • Initial amount: $5000
  • Growth factor: 6.2% = 0.062
  • Amount after it doubles: $10,000

    • Write a model for the tuition using the formula y equals a. b to the xth power
  • 10,000 = 5,000 (1 + .062)t
  • Divide both sides by 5000: 2 = (1 +0 .062)t
  • Change to logarithm form.
  • log 1.062   2 = t

Practice 3, Part Two

In 2000, the tuition to attend a state university was $5,000. The average increase per year since has been 6.2%. How long will it take for tuition to double?

  • 3 lines Line 1: 10 comma 000 equals 5000 times open paren 1 plus .062 close paren to the tth power Line 2: 2 equals open paren 1 plus .062 close paren to the tth power Line 3: the log base 1.062 of 2 equals t

  • Use change-of-base formulathe fraction with numerator log and denominator the log equals t
  • t = ______(Fill in the blank) years rounded to the nearest year

Answer:

  • the fraction with numerator log open bracket 2 and denominator the log 1.062 equals t
  • t = 12 years rounded to the nearest year