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valentina_108 [34]
3 years ago
7

A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues,

what will be the population of moose after 12 years?
years=x population =y
0,40
1,62
2,96
3,149
4,231
Mathematics
1 answer:
Alika [10]3 years ago
7 0

The population of the moose after 12 years is 7692

Step-by-step explanation:

The form of the exponential growth function is y=a(b)^{x} , 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

∵ 40=a(b)^{0}

- 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

∴ y=40(b)^{x}

∵ At x = 1 , y = 62

- Substitute them in the form of the equation above

∵ 62=40(b)^{1}

∴ 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 y=40(1.55)^{x}

To find the population of moose after 12 years substitute x by 12 in the equation

∵ y=40(1.55)^{12}

∴ 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

#LearnwithBrainly

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