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.

Question

Week

Weight (in pounds)

0 5000
1 6400
2 7800
3 9200

Answer 1

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.