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Exponential Growth & Decay:

Learn about exponential growth and decay equations, with examples on calculating future values and percentages. Explore population, investment, and depreciation scenarios. 8

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Exponential Growth & Decay:

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  1. Exponential Growth & Decay: Writing the Equation

  2. Exponential growth occurs when values are increasing. The base will be greater than 1. • Exponential decay occurs when values are decreasing. The base will be between 0 and 1or greater than 1 with a negative exponent. If growing by a rate(doubling, tripling): Initial amount Rate of change

  3. Example 1: The population of termites in a house triples every month. If there were 20 termites to begin with, how many termites will there be at the end of one year? f(x) = a∙bx f(x) = 20∙(3)12 f(x) = 10,628,820

  4. If growing/decaying by a percent: Important: write the rate as a decimal (i.e. 10% = 0.10)

  5. Clara invests $5000 in an account that pays 6.25% interest per year. After how many years will her investment be worth $10,000? Step 1: Write a function to model the growth in value of her investment. A = a(1 + r)t Exponential growth function. 10000 = 5000(1 + 0.0625)t 10000 = 5000(1.0625)t

  6. A city population, which was initially 15,500, has been dropping by 3% each year. What is the population of the city after 10 years? Exponential decay function. P(t) = a(1 – r)t P(t) = 15,500(1 – 0.03)10 P(t) = 15,500(0.97)10 P(t) = 11,430.07

  7. Write the equation • Alfred purchased a certain model of car for $26,000 that is known to depreciate 15% annually. What will the value of the car be in 7 years? When will the value of the car be approximately $13,572?

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