I need you show me your answer for number 47
1 answer:
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Answer:
Option A is correct.
is the equation represent the point slope form gives the plant's height at any time.
Step-by-step explanation:
Point slope intercept form: For any two points and
then,
the general form
for linear equations; where m is the slope given by:
Consider any two points from the table;
let A= (2 , 16) and B =(4, 32)
First calculate the slope of the line AB:
= 8
Therefore, slope of the line m = 8
Then,
the equation of line is:
Substitute the value of m=8 and (2, 16) above we get;
Therefore, the equation in point slope form which gives the plant's height at any time is; , where x is the time(months) and y is the plant height (cm)
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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