MATH SOLVE

4 months ago

Q:
# A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 2/5 the height on each successive bounce. a. Write a function representing the rebound height for each bounce. b. Graph the function. c. After how many bounces would a new softball rebound less than 1 inch?

Accepted Solution

A:

Part A:

For this case we have a function of the form:

[tex]y = A * (b) ^ x [/tex]

Where,

A: initial height

b: decrease rate

x: number of bounces

Substituting values we have:

[tex]y = 25 * (2/5) ^ x [/tex]

Rewriting:

[tex]y = 25 * (0.40) ^ x [/tex]

Answer:

[tex]y = 25 * (0.40) ^ x [/tex]

Part b:

See attached image

Part c:

By the time the height is less than 1 inch we have:

[tex]25 (0.40) ^ x \ \textless \ 1 [/tex]

From here, we clear x:

[tex](0.40) ^ x \ \textless \ 0.04 [/tex]

Logarithm on both sides:

[tex]x * log (0.40) \ \textless \ log (0.04) [/tex]

Rewriting:

[tex]x * (- 1.39794) \ \textless \ (-0.39794) [/tex]

[tex]x\ \textgreater \ (-0.39794) / (-1.39794) [/tex]

[tex]x\ \textgreater \ 3.513 [/tex]

Answer:

x> 3.513 or x = 4

For this case we have a function of the form:

[tex]y = A * (b) ^ x [/tex]

Where,

A: initial height

b: decrease rate

x: number of bounces

Substituting values we have:

[tex]y = 25 * (2/5) ^ x [/tex]

Rewriting:

[tex]y = 25 * (0.40) ^ x [/tex]

Answer:

[tex]y = 25 * (0.40) ^ x [/tex]

Part b:

See attached image

Part c:

By the time the height is less than 1 inch we have:

[tex]25 (0.40) ^ x \ \textless \ 1 [/tex]

From here, we clear x:

[tex](0.40) ^ x \ \textless \ 0.04 [/tex]

Logarithm on both sides:

[tex]x * log (0.40) \ \textless \ log (0.04) [/tex]

Rewriting:

[tex]x * (- 1.39794) \ \textless \ (-0.39794) [/tex]

[tex]x\ \textgreater \ (-0.39794) / (-1.39794) [/tex]

[tex]x\ \textgreater \ 3.513 [/tex]

Answer:

x> 3.513 or x = 4