- For problem 1, use the Growth and Decay Function: A(t) = a(1 + r)^t. The equation is N(l) = 2 * (1.20)^l, where N is nose length in inches and l is the number of lies. After 20 lies, his nose will be approximately 76.68 inches long. He would need to tell 18 lies for his nose to be longer than 3 ft (36 inches).
- For problem 2, the transformed function is y = -2^(x-3) - 4.
- For problem 3, use the Compound Interest Function: A = P(1 + r/n)^(nt). After 4 years, he would have $586.09. It would take him approximately 17.42 years to double his money.
- For problem 4, the distance from the house after n jumps is modeled by D(n) = 3 * (1/2)^n. After 10 jumps, he will be 0.00293 ft from his house. He will never make it to the house because the distance approaches zero but never reaches it (asymptotic behavior).
- For problem 5, the number of people told on the nth passing is 2^n. On the 10th passing, 1024 people will be told the secret.
- For problem 6, use the Growth and Decay Function with decay: A(t) = 80 * (1 - 0.035)^t. The population will drop below 15 lions after approximately 47.8 years. After 4 years, there will be approximately 69 lions left.
Parent Tip: Review the logic above to help your child master the concept of practice worksheet exponential functions answer key.
