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Another Look at Exponential Functions and What They Mean!

This exploration dives into exponential functions, illustrated by an antique coin's value increasing over time. The relationship between time and value is represented mathematically, starting with initial conditions and a common ratio, calculated using graphing technology. By analyzing specific data points, we determine the time required for the coin's value to double and look into alternative representations of this function. Real-world applications are highlighted, including investment growth and property appreciation, illustrating the importance of understanding these mathematical concepts.

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Another Look at Exponential Functions and What They Mean!

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  1. Another Look at Exponential Functions and What They Mean! Exponent Guy

  2. An antique coin appreciates in value the older it gets. The following data shows that the value of a certain coin for every year since it was purchased. a) Using a graphing calculator with Diagnostics turned on, determine the function for this relationship. a initial value, when x = 0 b common ratio (app by 15%)

  3. How long does it take for the coin to double in value?

  4. Now if we take into consideration these two points (0 , 3) and (5, 6) as two points on the curve and replace the doubling effect as 2 for the base, how else can we represent this scenario? 5 is the time it will take to double. 3is the initial value when x = 0 2 is the base to show the price is doubling.

  5. Determining a Function from a Table Try Page 136 # 30

  6. More Examples: 1. An investment triples every six years. If you invest $2500, how much will it be worth after 25 years? After 25 years, the $2500 investment would be worth $243, 189.73 2. A house appreciates by 10% every 4 years. How much would a $100,000 house be worth in 20 years? After 20 years, the house could sell for $161, 051.

  7. Try Page 136 # 31, 32, 35, 39 & Page 150 # 16, 18, 19, 22, 24, 27

  8. The More Practice, the Better! Page 150 # 16, 18, 19, 22, 24, 27 & Page 160 # 15, 18, 21, 24, 25

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