Tanya runs a catering business. based on her records, her weekly profit can be approximated by the function latex: f\left(x\right)=2x^2-44x-150 f ( x ) = 2 x 2 − 44 x − 150 , where latex: x x is the number of meals she caters. if latex: f(x) f ( x ) is negative, it means that the business has lost money. what is the number of meals that tanya needs to cater in order to break-even?

The function

is a parabola concave up, whose solutions are

from here, you can use the quadratic formula

to find that the solutions of the parabola are

So, the parabola is positive if (which wouldn't make sense in our case) or

So, if Tanya caters 25 meals she breaks even, and starting with the 26th meal she will begin to profit.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752