The table below shows the weight of a baby whale at birth and for the first three weeks of its life. Determine the linear equation that models this data and predict the baby whales weight at 5 weeks.
Week
Weight (in pounds)
0 5000
1 6400
2 7800
3 9200
To determine the linear equation that models this data, we can use the formula for the equation of a straight line:
y = mx + b
where y represents the weight of the baby whale (in pounds) and x represents the number of weeks. We need to find the values of m and b.
Let's use the data for the first three weeks to determine the values of m and b.
Using the points (0, 5000) and (1, 6400), we can find the slope (m):
m = (y2 - y1) / (x2 - x1)
= (6400 - 5000) / (1 - 0)
= 1400 / 1
= 1400
Using the slope-intercept form of the equation (y = mx + b), we can substitute the slope (m = 1400) and one of the given points (0, 5000) to solve for b:
5000 = 1400(0) + b
5000 = b
So the value of b is 5000.
Therefore, the linear equation that models the data is:
y = 1400x + 5000
To predict the baby whale's weight at 5 weeks, we substitute x = 5 into the equation:
y = 1400(5) + 5000
y = 7000 + 5000
y = 12000
Therefore, the predicted weight of the baby whale at 5 weeks is 12,000 pounds.
To determine the linear equation that models the data, we can use the formula for the equation of a straight line, which is y = mx + b. In this case, the weight (y) will depend on the week (x). We can use the first three data points to calculate the slope (m) and the y-intercept (b).
Let's start by calculating the slope:
m = (y₂ - y₁) / (x₂ - x₁)
Using the data points (0, 5000) and (1, 6400):
m = (6400 - 5000) / (1 - 0)
m = 1400 / 1
m = 1400
Now, let's calculate the y-intercept (b). We can use any of the given data points, so let's use (0, 5000):
y = mx + b
5000 = 1400(0) + b
5000 = b
So, the y-intercept (b) = 5000.
Now we can write the equation:
y = mx + b
y = 1400x + 5000
To predict the baby whale's weight at 5 weeks (x = 5), we substitute x = 5 into the equation:
y = 1400(5) + 5000
y = 7000 + 5000
y = 12000
Therefore, the predicted weight of the baby whale at 5 weeks is 12,000 pounds.