Mathematics High School

as a town gets smaller the population of its high school decreases by 5% each year. The senior class has 160 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation without graphing. Write an equation to represent the situation. Let n be the number of years before the class will have 100 students.

As A Town Gets Smaller The Population Of Its High School Decreases By 5% Each Year. The Senior Class

Answers

Answer 1

Answer:

T_n = 160(0.05)^(n - 1)

At T_n = 100, n = 1 year

Step-by-step explanation:

We will use geometric progression to solve this question.

Formula for nth term of a GP is;

T_n = ar^(n - 1)

We are told the population of its high school decreases by 5% each year.

This means r = 0.05

senior class has 160 students. Thus a = 160

Thus,T_n = 160(0.05)^(n - 1)

Where n is number of years after now.

We want to find the number of years before the class will have 100 students

Thus;

160(0.05)^(n - 1) = 100

(0.05)^(n - 1) = 100/160

(n-1)In 0.05 = In (100/160)

-2.9957(n - 1) = -0.47

(n - 1) = 0.47/2.9957

n = 1 + 0.1569

n = 1.1569

Approximating to the nearest whole number gives n = 1

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

Which of the following is the correct expanded form for the series below?
4
Σ-22
»=0
O-1-2-4-8-16
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Answers

Answer:

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Step-by-step explanation

The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

What is an exponent in math?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

the  series Σ-2^n, n = 0 to 4.

now, we have to find,

the correct expanded form for the series ,

as , we get,

the value of n = 0 to 4

so, putting the value of n = 0,1,2,3,4

we get the series as,

Σ-2^n

= -2^0 + (-2)^1 + (-2)^2 + (-2)^3 + (-2)^4

= 1 -2 + 4 - 8 +16

Hence, The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

To learn more on exponent number click:

brainly.com/question/19467739

#SPJ7

wou help video
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Answers

Answer:

The image is (-18,0)

Step-by-step explanation:

Here, we want to find the image of the given point after dilation by the given scale factor

Mathematically, given a point with the pre-image (x,y) going under the dilation of scale factor k, centered at the origin, the coordinates of the image will be;

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Answers

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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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Answers

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