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3 years ago

Rachel has been watching the number of alligators that live in her neighborhood. The number of alligators changes each week.

Mathematics

1 answer:

exis [7]3 years ago

8 0

Answer:

f(x) = 48(0.5)^n - 1 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of alligators changes each week

∵ The number in week 1 is 28

∵ The number in week 2 is 24

∵ The number in week 3 is 12

∵ The number in week 4 is 6

∴ The number of alligators is halved each week

∴ The number of alligators each week = half the number of alligators

of the previous week

- The number of alligators formed a geometric series in which the

first term is 48 and the constant ratio is 1/2

∵ Any term in the geometric series is Un = a r^(n - 1), where a is the

first term and r is the constant ratio

∴ f(n) = a r^(n - 1)

∵ a = 48 ⇒ The number of alligators in the first week

∵ r = 1/2 = 0.5

∴ f(x) = 48(0.5)^n - 1

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Recursive equation for the pattern followed is given by,

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<h2>Step-by-step explanation:</h2>

In the question,

The number of interaction for 1 child = 0

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So,

We need to find out the pattern for the recursive equation for the given conditions.

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We see that,

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Therefore, on checking, we observe that,

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On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

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$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

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At,

n = 2

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

At,

n = 3

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At,

n = 4

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