Question

A construction company showed that the strength, y, of concrete, measured

by the percent of design strength attained, depends on the length of time, x,
(in days) since it was poured.

This value can be approximated by the equation y = 2.8x + 17.

a) What is the y-intercept? What does it mean in this setting? Your answer should tell something about the strength of concrete.

b) What is the slope? What does it mean in this setting? Your answer
should tell something about the strength of concrete.

c) How long does it take before y = 100?

Answer 1

a) y-intercept = 17; initial design strength percentage

b) slope = 2.8; increase in that percentage each day

c) 29.6 days to 100% design strength

Explanation:

a, b) The equation is in the form called "slope-intercept form."

y = mx + b

where the slope is m, and the y-intercept is b.

Your equation has a slope of 2.8 and a y-intercept of 17.

The y-intercept is the percentage of design strength reached 0 days after the concrete is poured. The strength of the concrete when poured is 17% of its design strength.

The slope is the percentage of design strength added each day after the concrete is poured. The concrete increases its strength by 2.8% of its design strength each day after it is poured.

__

c) To find when 100% of design strength is reached, we need to solve for x:

100 = 2.8x +17

83 = 2.8x

83/2.8 = x ≈ 29.6

The concrete will reach 100 percent of its design strength in about 30 days.