The table gives the average gestation period for selected animals and their corresponding average longevity. a. Graph the data in a scatter plot using the number of days for gestation as the independent variable x and the longevity as the dependent variable y . b. Use the data points (44, 8.5) and (620, 35) to write a linear function that defines longevity L x as a linear function of the length of the gestation period x . Round the slope to 3 decimal places and the y -intercept to 2 decimal places. c. Interpret the meaning of the slope in the context of this problem. d. Use the model from part (b) to predict the longevity for an animal with an 80-day gestation period. Round to the nearest year.
The table gives the average gestation period for selected animals and their corresponding average longevity. a. Graph the data in a scatter plot using the number of days for gestation as the independent variable x and the longevity as the dependent variable y . b. Use the data points (44, 8.5) and (620, 35) to write a linear function that defines longevity L x as a linear function of the length of the gestation period x . Round the slope to 3 decimal places and the y -intercept to 2 decimal places. c. Interpret the meaning of the slope in the context of this problem. d. Use the model from part (b) to predict the longevity for an animal with an 80-day gestation period. Round to the nearest year.
Solution Summary: The author explains how to graph the data in a scatter plot using the number of days for gestation as the independent variable x and the longevity
The table gives the average gestation period for selected animals and their corresponding average longevity.
a. Graph the data in a scatter plot using the number of days for gestation as the independent variable
x
and the longevity as the dependent variable
y
.
b. Use the data points (44, 8.5) and (620, 35) to write a linear function that defines longevity
L
x
as a linear function of the length of the gestation period
x
. Round the slope to 3 decimal places and the
y
-intercept
to 2 decimal places.
c. Interpret the meaning of the slope in the context of this problem.
d. Use the model from part (b) to predict the longevity for an animal with an 80-day gestation period. Round to the nearest year.
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
Is the function f(x) continuous at x = 1?
(z)
6
5
4
3.
2
1
0
-10
-9
-7
-5
-2
-1 0
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
○ The function f(x) is continuous at x = 1.
○ The right limit does not equal the left limit. Therefore, the function is not continuous.
○ The function f(x) is discontinuous at x = 1.
○ We cannot tell if the function is continuous or discontinuous.
Is the function f(x) shown in the graph below continuous at x = −5?
f(x)
7
6
5
4
2
1
0
-10
-9
-8 -7
-6
-5
-4
-3
-2
-1 0
1
2
3
4
5
6 7 8 9
10
-1
-2
-3
-4
-5
-6
-7
Select the correct answer below:
The function f(x) is continuous.
○ The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
○ We cannot tell if the function is continuous or discontinuous.
4. Evaluate the following integrals. Show your work.
a)
-x
b) f₁²x²/2 + x² dx
c) fe³xdx
d) [2 cos(5x) dx
e) √
35x6
3+5x7
dx
3
g) reve
√ dt
h) fx (x-5) 10 dx
dt
1+12
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