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...

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.