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Misha Larkins [42]
4 years ago
15

GIVEN THE FUNCTION F(X) =3X + 5 AND X SUCH THAT F(X)=38

Mathematics
1 answer:
umka21 [38]4 years ago
6 0

The value of X is 11.

<u>Step-by-step explanation</u>:

Given,

  • F(X) = 3X + 5   --------(1)
  • F(X) = 38    ------------(2)

Equating eq(1) and (2),

⇒ 3X+5 = 38

⇒ 3X = 38-5

⇒ X = 33/3

⇒ X = 11

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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}  \\ &#10;A = 120 000 000 * e^{0.1411}   \\ &#10;A = 120 000 000 * 1.15 \\ &#10;A = 138 000 000&#10;
Thus, the population will be 138 million in 2014

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Answer:

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Step-by-step explanation:

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