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salantis [7]
3 years ago
12

Brady dropped a bouncy ball from a height of 64 feet. After the second bounce, the ball reached a height of 36 feet. write a rul

e to represent the height of the ball after each bounce, then find the height after the fourth bounce
Mathematics
1 answer:
AveGali [126]3 years ago
8 0

Answer:

Height  = 20.248 ft

Step-by-step explanation:

We can model this process with an exponential function

Height = Initial_Height *(e)^(k*x)

Initial_Height  = 64 ft

Second bounce

x  = 2

36 ft = 64 ft *(e)^(2*k)

(e)^(2*k) = 0.5625

2* k = ln(0.5625)

k = -0.2877

Fourth bounce

x =  4

Height = 64 *(e)^(-0.2877*(4))

Height  = 20.248 ft

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<em>Answer:</em>

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<em>Step-by-step explanation:</em>

<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>

<em></em>

<em>A)</em>

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<em>B)</em>

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