**50 POINTS!!! WILL GIVE BRAINLIEST!!!**
1 answer:
<h3>Given</h3>
The values of two houses (in thousands of dollars)
A) the nature of the function, linear or exponential, that can be used to model the value after x years
B) the actual function f(x) that can be used in each case
C) f(25) for each house. Is there a significant difference?
<h3>Solution</h3>A) The oddball numbers give you a clue immediately that the value of house 1 will be best modeled by an exponential function.
The value of house 2 is increasing steadily at 9,000 per year, so is modeled by a linear function.
B) The ratio of values from a given year to the year before for house 1 is
... 294.58/286 = 1.03
A check for other years reveals the same ratio, so the exponential function can be written for house 1 as
... f(x) = 286·1.03^x . . . . . value of house 1
In part A we determined the year-to-year difference in value for house 2 is 9,000. That is the slope of the linear function. Then (in thousands), that function is
... f(x) = 286 +9x . . . . . value of house 2
C) After 25 years, the house values are (in thousands of dollars)
The value of house 1 has more than doubled in the same time that the value of house 2 has increased by about 79%. This is a significant difference.
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An exponential function will always outperform a linear function over a long enough time period.
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Answer:
a, c
Step-by-step explanation:
There are 3 linear factors, so the function is odd degree (cubic). The coefficients of x are all positive, so the function has the general shape of an increasing function, left-to-right. The three linear factors mean that the curve crosses the x-axis 3 times, changing sign each time.
The x-intercepts are the values of x that make the factors zero: -7, 3/2, 5. The shape of the function tells you it will be negative for x < -7. Between -7 and 3/2, it will be positive, since it changes sign at x=-7. It changes sign again at x=3/2, so will be negative for 3/2 < x < 5.
In short, the function will be negative at any point that has an odd number of function zeros to its right (taking multiplicity into account).
The function is negative on intervals (a) and (c).
