Question

The height of a young flower is increasing in a linear fashion. Its height t weeks after the first of this month is given by

[H = 2.1t + 4] millimeters. Identify the initial value and growth rate, and explain in practical terms their meaning.

A: Initial value = 2.1 mm, Growth rate = 4
B: Initial value = 4 mm, Growth rate = 2.1
C: Initial value = 2.1 mm, Growth rate = 1
D: Initial value = 4 mm, Growth rate = 2.1

Answer 1

The initial value refers to the height of the flower at t=0 weeks, which is 4 mm, and the growth rate is how much the flower height increases every week, which is 2.1 mm/week.

Step-by-step explanation:

The height of the young flower is described by a linear equation H = 2.1t + 4, where H is the height in millimeters and t is the time in weeks since the first of this month. The equation is in the slope-intercept form, which is y = mx + b, where m is the slope (rate of change), and b is the y-intercept (initial value when x=0). Therefore, the initial value is 4 mm (the height of the flower at t=0 weeks), and the growth rate is 2.1 mm/week (the amount the flower's height increases each week).