Question

An experiment compares the heights of two plants over time. a plant was 2 cm tall at the beginning of the experiment and grew 0.5 centimeters each day. the function f(t)=0.5t+2 represents the height of the plant in centimeters after t days.

The graph shows the height of the second plant, g(t) in centimeters, as a function of time t in days.

Part 1: which plant, f or g, was growing faster?

Part 2: Which plant, f or g, was taller to begin with?

Part 3: Which plant, f or g, was taller after 8 days?

Answer 1

Part 1: plant f

Part 2: plant g

Part 3: plant g

Explanation:

✔️First plant:

Function: f(t) = 0.5t + 2

where,

f(t) = height of plant

t = number of days

m = slope/rate of change = 0.5 cm/day

b = y-intercept/initial height = 2 cm

✔️Second Plant: using two points on the graph, (0, 5) and (16, 9), let's find b and m for the function of the second plant.

Slope/rate of change (m) = ∆y/∆x = (9 - 5)/(16 - 0) = 4/16 = 0.25

m = 0.25 cm/day

The y-intercept or initial height is the y-coordinate of the point where the line intercepts the y-axis = 5

b = 5 cm

Towbrute the equation of the function, substitute m = 0.25 and b = 5 into g(t) = mt + b

Thus:

g(t) = 0.25t + 5

Knowing these, let's answer the problem given:

Part 1: plant f was growing faster because it has a greater rate of change/slope (m) of 0.5 cm/day

Part 2: plant g was taller because it has a greater initial value/y-intercept (b) which is 5 cm

Part 3: To find out which plant was taller after 8 days, substitute t = 8 into the equation of each function:

Plant f: f(t) = 0.5t + 2

f(8) = 0.5*8 + 2 = 4 + 2

f(8) = 6 cm

Plant g: f(t) = 0.25t + 5

g(8) = 0.25*8 + 5 = 2 + 5

g(8) = 7 cm

Thus, plant g was taller after 8 days having 7 cm