Answer: h(x) = -1200x^2 + 1950x + 4950
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Work Shown:
f(x) = revenue from the north
f(x) = -750x^2 + 1500x + 2250
g(x) = revenue from the south
g(x) = -450x^2 + 450x + 2700
h(x) = total revenue, ie add the two revenues
h(x) = f(x) + g(x)
h(x) = (-750x^2+1500x+2250)+(-450x^2+450x+2700)
h(x) = -1200x^2 + 1950x + 4950
5 less than 162=162-5
=157
Product=18x157
=2826
Let us examine the speed of growth of the function. We have that the difference between successive terms is: 2, 4, 8, 16. These are powers of 2 and thus there is clearly an exponential increase in the parent function. In fact, the function can be modeled by f(x)=C+2^x where C is a constant.
We have that the new function is g(x). Translating upwards by 5 means that the new y-values are 5 units higher. Hence, we have that the pairs (x,f(x)) correspond to the pairs (x,f(x)+5) and thus the answer is that the f(x)/y-values will be increased by 5.
According to the above, we need to check the given values and see whether in some cases we have g(x)=f(x)+5; in layman's terms, we need to check whether for some x, the new y-value is bigger by 5 from the old one. This is the case only for (2,16) since the old point was (2,11).
