What is the answer and explanation
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The population of the moose after 12 years is 7692
Step-by-step explanation:
The form of the exponential growth function is , where
- a is the initial value
- b is the growth factor
The table:
→ x : y
→ 0 : 40
→ 1 : 62
→ 2 : 96
→ 3 : 149
→ 4 : 231
To find the value of a , b in the equation use the data in the table
∵ At x = 0 , y = 40
- Substitute them in the form of the equation above
∵
- Remember any number to the power of zero is 1 (except 0)
∴ 40 = a(1)
∴ a = 40
- Substitute the value of a in the equation
∴
∵ At x = 1 , y = 62
- Substitute them in the form of the equation above
∵
∴ 62 = 40 b
- Divide both sides by 40
∴ 1.55 ≅ b
∴ The growth factor is about 1.55
- Substitute its value in the equation
∴ The equation of the population is
To find the population of moose after 12 years substitute x by 12 in the equation
∵
∴ y ≅ 7692
The population of the moose after 12 years is 7692
Learn more:
You can learn more about the logarithmic functions in brainly.com/question/11921476
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We know that x > 2 ( or : x ≠ +/- 2 )
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )