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Answer:
The amount the business initially invested in 1991 is approximately;
A. $3,450
Step-by-step explanation:
The question relates to investment and finance
The parameters given are;
The annual interest rate on the business savings account = 3%
The amount the business had in the account at the end of 1996 = $4,000
The given formula used to determine the final amount in the savings account,
Where;
F = The final amount
p = The initial (principal) investment
r = The annual interest rate
t = The time in years
Therefore, we have;
The required information = The initial amount, 'p', the business invested in 1991
The time in years, 't', from 1991 to 1996 = 1996 - 1991 = 5
∴ The time in years from 1991 to 1996, t = 5 years
The final amount in 1996, F = $4,000
r = 3%
Plugging in the values in the given equation gives;
Therefore;
To the nearest dollar, the initial amount the business invested in 1991, p ≈ $3,450.
<h2>Hello!</h2>
The answer is:
C) They both have the same y-intercept.
<h2>Why?</h2>In order to find the correct option, we need to find the equation of the function g(x), and then, compare its y-intercept with the y-intercept of the f(x) function.
So,
- Finding the equation of the g(x):
Calculating the slope of the function, using the first two points (-1,8) and (1,0), we have:
Now, calculating the value of "b" using the first point (-1,8) and the slope of the function, we have:
So, the equation of g(x) is:
- Comparing the y-intercepts of f(x) and g(x):
Finding the y-intercept of f(x), by making "x" equal to 0, we have:
We have that the function f(x) has its y-intercept at "y" equal to 4.
Finding the y-intercept of g(x), by making "x" equal to 0, we have:
We have that the function g(x) has its y-intercept at "y" equal to 4.
Hence, we have that both functions have their y-intercepts at the same point, so, the correct option is:
C) They both have the same y-intercept.
Have a nice day!