Question

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

Answer:

The equation is $m(n) = 24(0.75)^{n}$

Step-by-step explanation:

Let the exponential function is $m(n) = a(b)^{n}$, where m is the angle of the swing forward and n is the number of swings.

Here, a and b are constants.

Now, for n = 1, m = 18 degrees and for n = 2, m = 13.5 degrees.

Therefore, the two equations that we can write are :

$18 = a(b)^{1} = ab$ ............. (1) and

$13.5 = a(b)^{2}$ ................. (2)

Now, solving the above two equations we get,

$\frac{ab^{2} }{ab} = \frac{13.5}{18} = 0.75$

⇒ b = 0.75

So, from equation (1) we get, $a = \frac{18}{0.75} = 24$

Therefore, the equation is $m(n) = 24(0.75)^{n}$ (Answer)