Question

A child starts a playground swing from standing and doesn't use her legs to keep swinging. On the first

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)