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Mnenie [13.5K]
3 years ago
15

Find the 8th term in the arithmetic sequence An=-2x+4

Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0

Answer:

a(8) = -12

Step-by-step explanation:

The 8th term in the sequence is when n = 8. Substitute x = 8 into the rule An=-2x+4.

a(8) = -2(8) + 4

a(8) = -16 + 4

a(8) = -12

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A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential gr
Rufina [12.5K]
The answer is 138 million.

Step 1. Calculate the growth rate.
Step 2. Calculate the population number in 2014.

We will use the formula for exponential growth:
A = P * eⁿˣ
where:
A - the final amount (value)
P - the initial amount (value)
e - the mathematical constant (e ≈ 2.72)
n - the growth rate
x - the time

Step 1:
A = 120 million = 120 000 000
P = 114 million = 114 000 000
n = ?
x = 1997 - 1991 = 6
Therefore:
120 000 000 = 114 000 000 * e ^{n*6} \\ e ^{n*6} =120 000 000 /114000000 \\ e ^{n*6} =1.05 \\
Logarithm both sides of the equation:
ln(e ^{n*6})=ln(1.05) \\ n*6*ln(e) = ln(1.05) \\ 6n=ln(1.05) \\ n = \frac{ln(1.05)}{6} \\ n = \frac{0.05}{6} \\ n = 0.0083

Step 2:
Now when we know the growth rate, it is easy to estimate the population in 2014
A = ?
P = 120 000 000
n = 0.0083
t = 2014 - 1997 = 17
A = 120 000 000 * e ^{0.0083*17}  \\ 
A = 120 000 000 * e^{0.1411}   \\ 
A = 120 000 000 * 1.15 \\ 
A = 138 000 000

Thus, the population will be 138 million in 2014

8 0
3 years ago
Genesis has an action figure collection. She keeps some in a display case and the rest on the wall. 253 of her action figures ar
Tcecarenko [31]

Answer:460

Step-by-step explanation:on delta math

3 0
2 years ago
How to turn 0.95 into a fraction
Amanda [17]

Move the decimal point to the right two place values, and set the number over 100

0.95 = 95/100

95/100 is your fraction answer.

Simplify it if asked. 95/100 = 19/20

~

3 0
3 years ago
Read 2 more answers
30. The perimeter of a rectangle is 292 feet. The length of the rectangle is 4 feet less than 5 times the width. What is the len
blondinia [14]
P = 2(L + W)
P = 292
L = 5W - 4

292 = 2(5W - 4 + W)
292 = 2(6W - 4)
292 = 12W - 8
292 + 8 = 12W
300 = 12W
300/12 = W
25 = W <=== width is 25 ft

L = 5W - 4
L = 5(25) - 4
L = 125 - 4
L = 121 <=== length is 121 ft
5 0
3 years ago
What is the slope of the line that has the equation 4x + 2y = 12?
Kay [80]
= -2


Im pretty sure
Best of luck hope I helped :)
3 0
2 years ago
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