Brad is correct.
Polynomials do not include negative exponents; this means there can be no variables in the denominator. If two polynomials do not divide evenly, the remainder is written as a fraction with the divisor (which can include a variable) in the denominator. This is not a polynomial.
a) The total monthly cost is the sum of the fixed cost and the variable cost. If q represents the number of cones sold in a month, the monthly cost c(q) is given by
c(q) = 300 + 0.25q
b) If q cones are sold for $1.25 each, the revenue is given by
r(q) = 1.25q
c) Profit is the difference between revenue and cost.
p(q) = r(q) - c(q)
p(q) = 1.00q - 300 . . . . . . slope-intercept form
d) The equation in part (c) is already in slope-intercept form.
q - p = 300 . . . . . . . . . . . . standard form
The slope is the profit contribution from the sale of one cone ($1 per cone).
The intercept is the profit (loss) that results if no cones are sold.
e) With a suitable graphing program either form of the equation can be graphed simply by entering it into the program.
Slope-intercept form. Plot the intercept (-300) and draw a line with the appropriate slope (1).
Standard form. It is convenient to actually or virtually convert the equation to intercept form and draw a line through the points (0, -300) and (300, 0) where q is on the horizontal axis.
f) Of the three equations created, we presume the one of interest is the profit equation. Its domain is all non-negative values of q. Its range is all values of p that are -300 or more.
g) The x-intercept identified in part (e) is (300, 0). You need to sell 300 cones to break even.
h) Profit numbers are
425 cones: $125 profit
550 cones: $250 profit
700 cones: $400 profit
Hi there! So the situation that we are talking about for this is compounding, because the population is growing.. The formula for compounding something is P(1 + r)^t, with P representing the initial amount, r representing the rate, and t representing the time in years. First off, let's add the rate into 1. 1.2% is 0.012 in decimal form. 1 + 0.012 is 1.012. Now, because we are looking for the population after 4 years. We raise 1.012 to the 4th power. 1.012^4 is 1.04887093274. It's a long decimal, but do not delete this number from your calculator. Now, we multiply that number by 38,300 in order to get 40,171.7567238 or 40,172 when rounded to the nearest whole number. There. The population of Huntersville will be 40,172 people in 4 years.
