14. You deposit $400 in a savings account that earns 7% interest compounded annually.
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<u>Answer</u>
Graph D represents the national debt of the country over the next years.
<u>Solution-</u>
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,
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
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.
The equation has one extraneous solution which is n ≈ 2.38450287.
Given that,
The equation;
We have to find,
How many extraneous solutions does the equation?
According to the question,
An extraneous solution is a solution value of the variable in the equations, that is found by solving the given equation algebraically but it is not a solution of the given equation.
To solve the equation cross multiplication process is applied following all the steps given below.
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y
with 0 and solve for x. The graph of the equation is attached.
n ≈ 2.38450287
Hence, The equation has one extraneous solution which is n ≈ 2.38450287
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