Mathematics: A Super Happy Fun Ball is dropped from a height of 4 feet and rebounds 4 5 of the distance from which it fell. How many times will it bounce before its rebound is less than 1 foot

X= 44 – y is the right equation....

A Super Happy Fun Ball is dropped from a height

BreBreDoeCCx

13.02.2022

More than 6.21 times

Step-by-step explanation:

The common ratio $r=\dfrac{4}{5}$

Distance of first bounce

$a_1=4\times \dfrac{4}{5}=\dfrac{16}{5}$

Second bounce

$a_2=ar^{n-1}=\dfrac{16}{5}(\dfrac{4}{5})^{2-1}\\\Rightarrow a_2=\dfrac{16}{5}(\dfrac{4}{5})$

n bounce

$a_n=ar^{n-1}\\\Rightarrow a_n=\dfrac{16}{5}(\dfrac{4}{5})^{n-1}$

Now the nth bounce will be less than 1 feet

$\dfrac{16}{5}(\dfrac{4}{5})^{n-1}$

Applying logarithms on both sides we get

$(n-1)\ln \dfrac{4}{5}\dfrac{\ln\dfrac{5}{16}}{\ln \dfrac{4}{5}}+1$

The inequality changes as both $\ln\dfrac{5}{16}$ and $\ln \dfrac{4}{5}$ are negative numbers.

So,

n6.21

Hence, the number of bounces is more than 6.21 times.

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