Question

A child on a swing is pushed just once. The child moves a distance of 10
feet the first swing, and then only 83%
as much as the previous swing for each one after.

Which of the following sequences expresses the distance the child travels n
swings after the first?
A
an=10(0.83)n
B
an=(10.83)n
C
an=(10.83)n
D
an=10(0.83)n

Answer 1

the distance the child travels n  swings after the first is  $Distance = 10(0.83)^n$ . Options A) and D) are identical , so kindly match $Distance = 10(0.83)^n$  with your answer !

Step-by-step explanation:

Here we have , A child on a swing is pushed just once. The child moves a distance of 10  feet the first swing, and then only 83%  as much as the previous swing for each one after. We need to find Which of the following sequences expresses the distance the child travels n  swings after the first . Let's find out:

Initially the distance is 10 feet from after the first swing . It's given that there is 83% as much as previous distance !

For first swing :

⇒ $Distance = S_0 =10(0.83)$

For second swing :

⇒ $Distance = S_1 =10(0.83)^2$

For third swing :

⇒ $Distance = S_2 =(10(0.83^2))(0.83) = (S_1)0.83$

⇒ $Distance = S_2 =10(0.83)^2$

So , For n swings :

⇒ $Distance = 10(0.83)^n$

Therefore , the distance the child travels n  swings after the first is  $Distance = 10(0.83)^n$ .