Aim: How do we apply the exponential function? Do Now: John bought an antique for $1000. The value of the antique has a 10% fixed increasing rate annually.

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Aim: How do we apply the exponential function? Do Now: John bought an antique for $1000. The value of the antique has a 10% fixed increasing rate annually. Find the value of the antique after a) 1 year b) 2 years c) 5 years d) 10 years HW: p.312 # 6,8,12 p.313 # 18,20,21,22,24

a) b) Part a) can be written as Part b) can be written as

From Do Now #1 & 2, we can derive a formula for exponential growth A = A 0 (1 + r) t A is the amount after certain number of years A 0 is the initial amount r is the rate t is the number of years

Use the formula to find the answers for # 3 and 4 A = 1000( ) 5 = 1000(1.1) 5 = 1000( ) = A = 1000( ) 10 = 1000(1.1) 10 = 1000(2.5937) =

Enrique won $10,000 and decided to use it as a “vacation fund.” each summer, he withdraws an amount of money that reduces the value of the fund by 7.5% from the previous summer. How much will the fund be worth after the tenth withdrawal? This problem is decay situation Use the formula A = A 0 (1 + r) t with A 0 = , r = – and t = 10. A = 10,000(1 – 0.075) 10 = 10,000(0.925) 10 = 4,585.82

To find the compound interest, we use the formula, n is number of times compounded per year. t is the number of years. If the interest compounded continuously, we use the formula

In a state park, the deer population was estimated to be 2000 and increasing continuously at a rate of 4% per year. If the increase continues at that rate, what is the expected deer population in 10 years? Use the formula A = A 0 e rt. Let A 0 = 2000, r = 0.04, and t = 10. A = 2000e 0.04(10) = 2000e 0.4 = 2984

The decay constant of radium is – per year. How many grams will remain of a 50-gram sample of radium after 20 years? Since change takes place continuously, use the formula A = A 0 e rt. Let A 0 = 50, r = – and t = 20 grams