# How do I solve the following word problem?A botanist watched the growth of a lily. At 3 weeks, the lily was 4 inches tall. Four weeks later, the lily was 21 inches tall. Assuming the relationship...

How do I solve the following word problem?

*A botanist watched the growth of a lily. At 3 weeks, the lily was 4 inches tall. Four weeks later, the lily was 21 inches tall. Assuming the relationship is linear:*

*(a) Write an equation to show the grow pattern of this plant.*

*(b) How tall was the lily at the 5.5 mark?*

*(c) Is there a restriction on how high the plant will grow? Does your equation show this?*

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### 1 Answer

First, assign the variables.

x: time of growth (weeks)

y: height of lily (inches)

Next, use the given information to write two points.

At 3 weeks, the lily was 4 inches tall. (3, 4)

Four weeks later, the lily was 21 inches tall. (7, 21)

Now use these points to calculate the slope of the line.

m = (y2 - y1) / (x2 - x1)

m = (21 - 4) / (7 - 3)

m = 17/4 = 4.25

Now substitute 4.25 in for m in the equation. Also, select one of the points and substitute 3 in for x and 4 in for y. Solve for b.

y = mx + b

4 = 4.25 * 3 + b

4 = 12.75 + b

-8.75 = b

The equation that represents the growth pattern of this plant is...

**(a) y = 4.25x + -8.75**

To find the height of the lily after 5.5 weeks, substitute 5.5 in for x and solve for y.

y = 4.25 * 5.5 + -8.75

y = 14.625

At the 5.5 mark, the height of the lily will be...

**(b) 14.625 inches**

There is a restriction on how high the plant will grow. A plant will not grow to an unlimited height. For example, after 75 weeks, the lily would reach a height of 310 inches. That's over 25 feet tall.

The equation does not show these restrictions. By definition, a linear equation continues indefinitely in both directions. Lilies grow to a maximum height of only a few feet.

**(c) Yes, there is a restriction. No, the equation does not reflect this restriction.**