Question

When Mustafa threw a beach ball to his friend, its horizontal velocity changed as it traveled through the air. The relationship between the elapsed time, tttt, in seconds, since Mustafa threw the ball, and its horizontal velocity, V(t)V(t)V(t)V, left parenthesis, t, right parenthesis, in cm/s\text{cm/s}cm/sstart text, c, m, slash, s, end text, is modeled by the following function: V(t)=4⋅(0.81)t Complete the following sentence about the percent change of the horizontal velocity of the ball. Every second, %\%%percent of horizontal velocity is the total horizontal velocity of the ball.

Answer 1

The rate at which the horizontal velocity of the ball changes every second is, 19%.

Explanation:

The exponential decay function is given by:

`y=a(1-r)^(t)`

Here,

y = final value

a = initial value

r = decay rate

t = time

The relationship between the elapsed time, t, in seconds, since Mustafa threw the ball, and its horizontal velocity, V (t) is:

`V(t)=4\cdot (0.81)^(t)`

The expression for the horizontal velocity of the ball represents the exponential decay function.

On comparing the two equations we get:

`1-r=0.81\\r=1-0.81\\r=0.19`

Thus, the rate at which the horizontal velocity of the ball changes every second is, 19%.