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Mumz [18]
3 years ago
6

The capacity of a school is 1100 students and the current enrollment is 980 students. If the student population increases at a r

ate of 5 percent per year, what is the smallest integer $n$ such that the enrollment will exceed the capacity in $n$ years?
Mathematics
2 answers:
Mazyrski [523]3 years ago
4 0

Answer:

3 years

Step-by-step explanation:

In this problem, the initial number of students at time t = 0 is

n_0 = 980

We know that the number of students increases by 5 % every year. This means that we can write the student's population as

n(t)=(1.05)^t n_0

where

t is the time, measured in years

Here we want to find after how many years t the student's population will exceed the maximum capacity of the school, which is

N = 1100

To solve the problem, we just put n = 1100 and we solve for t. We find:

1100 = (1.05)^t n_0\\t=log_{1.05} (\frac{1100}{980})=2.37 y

Which means that the student's population reaches the maximum capacity of the school after 2.37 years. Since we want this number to be an integer, this means that the enrollment will exceed the capacity in 3 years.

Vilka [71]3 years ago
4 0

Answer:

3 years

Step-by-step explanation:

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Answer:

1. x = 67.5

2. x = 2.5

3. x = 35.2

4. x = 2.0

5. x = 17.0

Step-by-step explanation:

Question 1

The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:

2x/9 = 15

2x = 9(15)

Next solve for x:

2x = 135

x = 67.5

Question 2

The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:

20x/8.7 = 5.8

20x = 8.7(5.8)

Next, solve for x:

20x = 50.46

x = 2.523

Round to the nearest tenth:

x = 2.5

Question 3

The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:

5x/16 = 11

5x = 11(16)

Next, solve for x:

5x = 176

x = 35.2

Question 4

The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:

0.5x/0.06 = 17

0.5x = 17(0.06)

Next, solve for x:

0.5x = 1.02

x = 2.04

Round to the nearest tenth:

x = 2.0

Question 5

The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:

29(44)/x = 75

29(44) = 75x

Next, solve for x:

1276 = 75x

x = 17.0133

Round to the nearest tenth:

x = 17.0

7 0
2 years ago
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