A gardener measured the heights of two plants at the end of every week. The function y=3x+8.5 gives the height of plant A in centimeters at the end of x weeks. The function y=2.5x + 14.5 gives the height of PlantB in centimeters at the end of x weeks

Answer 1

Based on the given functions:

For Plant A: y = 3x + 8.5
For Plant B: y = 2.5x + 14.5

These functions represent linear equations where 'y' is the height in centimeters of the plants at the end of 'x' weeks.

According to the equation for Plant A, this plant grows at a rate of 3 centimeters per week, starting at an initial height of 8.5 centimeters when x = 0 (which could be the height at the beginning of the observation or planting).

For Plant B, the growth rate is 2.5 centimeters per week, starting at an initial height of 14.5 centimeters when x = 0.

To find the height at a specific number of weeks, simply substitute the value of 'x' (the number of weeks) into each function. For example, to find the height of each plant after 4 weeks:

For Plant A at the end of 4 weeks:
y = 3(4) + 8.5
y = 12 + 8.5
y = 20.5 cm

For Plant B at the end of 4 weeks:
y = 2.5(4) + 14.5
y = 10 + 14.5
y = 24.5 cm

Therefore, according to the given linear models, at the end of 4 weeks, Plant A would be 20.5 cm tall, and Plant B would be 24.5 cm tall.

It's also interesting to note when or if Plant A will ever surpass Plant B in height. For determining that, you will need to find the point at which both plant heights are equal:

3x + 8.5 = 2.5x + 14.5

Solving for x gives us the time in weeks when both plants will have the same height. Subtracting 2.5x from both sides gives:

0.5x = 6

Now, divide both sides by 0.5 to solve for x:

x = 6 / 0.5
x = 12 weeks

So at the end of 12 weeks, both Plant A and Plant B will have the same height. To find out what that height is, plug x = 12 back into either of the original equations:

y = 3(12) + 8.5
y = 36 + 8.5
y = 44.5 cm

So, after 12 weeks, both plants will be 44.5 cm tall. After this point, since Plant A is growing faster (3 cm per week) compared to Plant B (2.5 cm per week), Plant A will be taller than Plant B.