Question

A country is planning to decrease government spending in order to reduce the national debt. If the outlined changes are put into place, the country's debt will decrease exponentially by one-third each year. The current debt is $60 billion in U.S. dollars. If this trend continues, which graph represents the national debt of the country over the next several years?
A. https://cdn.app.edmentum.com/EdAssets/f5b53b61e8f5457485a14959c83ec160?ts=636270882149370000

B. https://cdn.app.edmentum.com/EdAssets/2470791ed62e4ab39622aed23b2d5253?ts=636270882670400000

C. https://cdn.app.edmentum.com/EdAssets/daf6c2be09cb48389301d40117ffb118?ts=636270882468230000

D. https://cdn.app.edmentum.com/EdAssets/ced65d99c879463db10ea2d443266b3d?ts=636270882324100000

Answer 1

Answer

Graph D represents the national debt of the country over the next years.

Solution-

The country's debt will decrease exponentially by one-third each year.

Current debt is $60 billion.

This problem can be treated as an exponential decay problem.

The general exponential decay function is,

$y=a(r)^{-x}$

Where,

a = initial value,

r = rate of change,

-ve sign of x represents the decrease in value of y as x increases.

Here, the rate of change is 3 as each year the debt becomes on third, and initial value of debt is $60, so

$y=60(3)^{-x}$

Plotting a graph taking number of year on x-axis and debt on y-axis, we can generate a graph for this function.

Putting different values of x, we can get the values of y. So the graph must have (0, 60), (1, 20), (2, 6.66), (3, 2.22), (4, 0.74), (5, 0.24) points on it.

Option B and C are incorrect, as they do not start from 60. (they don't have (0,60) on their curve)

Between option A and D, curve in D has all the points on it. So D is the correct graph.

Answer 2

Answer: Its C for Plato users

Step-by-step explanation: