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?

 

Asked on by catd1115

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samhouston | Middle School Teacher | (Level 1) Associate Educator

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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.

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