Question

A company collected data for the number of text messages sent and received using a text-message application since October 2011. The table shows the number of text messages sent and received in billions over time. The data can be modeled by a quadratic function. Which function best models the data?

A. n(t) = -0.002t^2 + 0.55t + 5.02

B. n(t) = 0.072t^2 - 0.15t + 2.73

C. n(t) = -0.002t^2 + 5.02

D. n(t) = 0.072t^2 + 2.73

Answer 1

Answer:

B. n(t) = 0.072t^2 - 0.15t + 2.73

Step-by-step explanation:

Plot data as pair of coordinates where t =x and n(t)=y

Use a graph tool to plot the coordinate points and join the points with a smooth curve

From the answers, test for the function that fits the points as plotted on the tool.

In this case, the function that fits the plot of the data is ;

n(t) = 0.072t^2 - 0.15t + 2.73

See attached;

Answer 2

The function that best used to model this situation is n(t) = 0.072t² - 0.299t + 2.57

Quadratic function

Quadratic function is in the form:

• y = ax² + bx + c

where a, b, c are constants.

Let n(t) represent the number of text at time t months.

It is given by:

n(t) = at² + bt + c

At point (5, 3):

• 3 = a(5)² + 5b + c
• 25a + 5b + c = 3    (1)

At point (20, 27):

• 27 = a(20)² + 20b + c
• 400a + 20b + c = 27    (2)

At point (40, 112):

• 112 = a(40)² + 40b + c
• 1600a + 40b + c = 112    (3)

a = 0.072, b = -0.29, c = 2.57

n(t) = 0.072t² - 0.299t + 2.57

The function that best used to model this situation is h(t) = -4.9t² + 295 + 2

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