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s344n2d4d5 [400]
3 years ago
13

Lenmana started studying how the number of branches on her tree grows over time. The number of branches increases by a factor of

11/6 every 3.5 years, and can be modeled by a function, N, which depends on the amount of time, t (in years).
When Lenmana began the study, her tree had 48 branches.

Write a function that models the number of branches t years since Lenmana began studying her tree.

N(t)=
Mathematics
1 answer:
Ad libitum [116K]3 years ago
7 0

Answer:

N(t) = 48 * 11/6^{\frac{t}{3.5} }

Step-by-step explanation:

The formula for <u>exponential growth</u> is y = ab^x.

To write this equation, we know it has to start with 48 (which is the variable a). We need to add the rate of growth. This is 11/6 (which is variable b). But we also need to account for the "every 3.5 years" part, so divide the x as an exponent by 3.5.

N(t) = 48 * 11/6^(t/3.5)

This equation is easy to test, and it's a good idea to test it after you write it. For example, after 3.5 years we know that it should have 48*11/6 branches. Does our equation work? Yes.

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the sum of three number number in an artithmetic product is 21. if second number isreduced by 1 and third term is increased by 1
grin007 [14]

The three numbers will be 12, 7, 2 and 3, 7, 11.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

Let the three consecutive numbers be a, a + d, and a + 2d

The sum of three numbers which are consecutive terms of an A.P. is 21.

a + a + d + a + 2d = 21

3(a + d) = 21

a = 7 - d

If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.

Then the number will be a, a + d − 1, a + 2d + 1. Then we have

\rm \dfrac{a + d - 1}{a} = \dfrac{a + 2d + 1}{a + d - 1}

On simplifying, we have

36 = a (8 + d)

a² - 15a + 36 = 0

On factorizing, the value of a will be

a² - 15a + 36 = 0

a² - 12a  - 3a + 36 = 0

(a - 12)(a - 3) = 0

a = 3, 12

If a = 12, then the value of d will be

d = 7 - 12

d = -5

If a = 3, then the value of d will be

d = 7 - 3

d = 4

Then the three numbers will be 12, 7, 2 and 3, 7, 11.

More about the sequence link is given below.

brainly.com/question/21961097

#SPJ1

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natta225 [31]
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4 0
3 years ago
Perform the indicated operation.(4r/r+3) - (5/r)
Aleks [24]

Answer:

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Step-by-step explanation:

To solve this problem, we will proceed the following way, writing down the common multiple of the denominators.

\frac{4r}{r+3} -\frac{5}{r} =\frac{4r(r)-5(r+3)}{r(r+3)} =\frac{4r^{2}-5r-15 }{r(r+3)}

Thus, the answer is 4r² - 5r - 15 / r(r+3)

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lisov135 [29]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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