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2 answers:
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Answer:
S'(x)=-0.006x2+0.8x+9
Step-by-step explanation:
The rate of change of the sales S(x) with respect to the amount of money spent on advertising x is then the derivative of S(x) with respect to x. What we have to calculate is S'(x).
We know that the derivative of is
(where a is a constant), and the derivative of a sum is the sum of the derivatives, so we can calculate the derivative of each term independently:
S'(x)=(−0.002x3 + 0.4x2 + 9x + 500)'=(−0.002)(3)x2 + (0.4)(2)x + 9
Which means:
S'(x)=-0.006x2+0.8x+9
Answer:
The horizontal line is the asymptote
Step-by-step explanation:
This is an exponential function.
An asymptote is the line a function approaches but never touches.
Here, is the horizontal line that is asymptote of the function.
<u>Note:</u> <em>Normally, y=0 is the asymptote of a parent exponential function, since this graph is parent function shifted 2 units up, the asymptote becomes y=2</em>