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sergeinik [125]
2 years ago
11

In 1992, South Dakota's population was 10 million. Since then, the population has grown by 1.4% each year. Based on this, when w

ill the population reach 20 million?
Mathematics
2 answers:
ella [17]2 years ago
8 0

Answer:

  • 49.9 years or 50 years later.
  • At year : 2042

Explanation:

use compound interest formula:  \sf \boxed{ \sf P ( \sf 1 + \dfrac{r}{100} )^n}

\rightarrow \s \sf 10( 1 + \dfrac{1.4}{100} )^n = 20

\rightarrow \sf ( 1.014) ^n = 2

\rightarrow \sf n( ln( 1.014) ) = ln(2)

\rightarrow\sf n = \dfrac{ln(2)}{ln( 1.014)}

\rightarrow\sf n = 49.8563 \ years

mel-nik [20]2 years ago
4 0

Answer:

General form of an exponential equation:  y=ab^x

where:

  • a is initial value
  • b is the base (or growth factor in decimal form)
  • x is the independent variable
  • y is the dependent variable
  • If b > 1 then it is an increasing function
  • If 0 < b < 1 then it is a decreasing function
  • Also b ≠ 0

Given information:

  • initial population = 10 million
  • growth rate = 1.4% each year

⇒ growth factor = 100% + 1.4% = 101.4% = 1.014

Inputting these values into the equation:

\implies y=10(1.014)^x

where y is the population (in millions) and x is the number of years since 1992

Now all we need to do is set y = 20 and solve for x:

\implies 10(1.014)^x=20

\implies 1.014^x=2

\implies \ln 1.014^x=\ln 2

\implies x\ln 1.014=\ln 2

\implies x=\dfrac{\ln 2}{\ln 1.014}

\implies x=49.85628343...

1992 + x = 2041.8562....

Therefore, the population will reach 20 million during 2041, so the population will reach 20 million by 2042.

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olga_2 [115]

Answer:

height ≈ 31 ft

Step-by-step explanation:

The illustration below will form a right angle triangle. He is standing 17 ft away from the base of the statue.  The angle of elevation from the ground to the top of the statue  is 61°. The height of the statue can be computed below.

adjacent side of the triangle = 17 ft

opposite side = a

Using SOHCAHTOA principle

tan 61° = opposite/adjacent

tan 61° = a/17

cross multiply

a = 17 tan 61°

a = 17 × 1.80404775527

a = 30.6688118396

a ≈ 31 ft

6 0
3 years ago
The olympics are held every four years. In 2016, the XXXI olympiad were held in Rio de Janeiro,Brazil. Determine the year of the
Anna007 [38]

Answer:

First Olympic held in year 1896.

Step-by-step explanation:

Number of Olympiad held in Rio = XXXI = 31st

Difference of years in two consecutive Olympiads = 4 years

Number of years spent in 31 Olympiads can be calculated by,

Number of years spent = (n - 1)d

Here n = number of Olympiads held

d = difference between two consecutive Olympiads

Number of years spent till 31st Olympiads = (31 - 1)×4

                                                                      = 120 years

Therefore, 1st Olympiad held in the year = 2016 - 120

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6 0
2 years ago
Here is my question please answer and give a good explanation: Which expression cannot be used to calculate the total amount pai
Ierofanga [76]
I'm pretty sure the answer is D. because I don't think anyone would want to take their total meal cost and then multiply it by their tip to make it even larger. You would just add the tip to the meal cost.
6 0
3 years ago
What number can replace the n in n/12 to make it equivalent to 1/2 ?<br> 6<br> 8<br> 9<br> 10
Ierofanga [76]

Answer:

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4 0
3 years ago
Read 2 more answers
A pizza has a diameter of 12 inches. Each piece has a central angle of radians. What is
Firlakuza [10]

Answer:

The area of one slice of pizza is 18 in²

Step-by-step explanation:

First we have to know that the 360 ​​° representing the circle expressed in radians are expressed as 2π

Now we must calculate the area of ​​the circle

a = π * r²

a = π * (12in)²

a = 144π in²

Now that we have the area of ​​the circumference we multiply it by (π/4) / (2π)

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The area of one slice of pizza is 18 in²

3 0
3 years ago
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