Question

An experiment compares the height of two plants over time. A plant was 2cm tall at the beginning of the experiment and grew 0.5 centimeters each day. The functions f(t)=0.5+2 represents the height of the plant in centimeters after t days . Which plant for f, or g was growing faster ?

Answer 1

Plant F;

Plant G;

Plant G

Explanation:

Given that:

Plant F :

f(t)=0.5x+2

From the growth graph given for the second plant ; plant G

Point 1 (0, 5) ; point 2(16, 9)

Slope = Rise / Run = (9 - 5) / (16 - 0) = 4 / 16 = 0.25

Intercept = 5 ( point where fitted line crosses the y-axis)

Linear slope intercept relation : y = mx + c

m = slope ; c = intercept

g(x) = 0.25x + 5

The slope value of plant F = 0.5

Slope value of plant G = 0.25

F > G

Hence, F is growing at a faster rate

The starting height is given by the intercept value of the two equations ;

Plant F, intercept = 2

Plant G, intercept = 5

G > F

Hence, G was taller, to begin with

Height after 8 days :

x = 8

f(8)=0.5(8)+2

f(8) = 4 +2 = 6

g(8) = 0.25(8) + 5

g(8) = 2 + 5 = 7

Hence, G was taller after 8 days