Question

Use two points to enter an equation for the function. Give your answer in the form a(b)^n. In the event that a = 1, give your answer in the form (b)^n. A child starts a playground swing from standing and doesn't use her legs to keep swinging. On the first swing she swings forward by 18 degrees, and on the second swing she only comes 13.5 degrees forward. The measure in degrees of the angle m(n) is an exponential function of the number n of swings. The equation is m(n) =

Answer 1

`m(n) = 24 (0.75)^n`

Explanation:

1) The two points are:

a) On the first swing she swings forward by 18 degrees: (1, 18)

b) On the second swing she only comes 13.5 degrees forward: (2,13.5)

2) The general equation using the form given is:

`m(n)=A(B)^n`

3) Substitute the two points:

`18=A(B)\\ \\ 13.5=A(B)^2`

4) Divide the second equation by the first one:

⇒ 13.5 / 18 = B

⇒ B = 0.75

5) Substitue B = 0.75 into the first equation:

18 = A (0.75) ⇒ A = 18 / 0.75 = 24

Hence, the equation is:

`m(n) = 24 (0.75)^n`