Answer:
Step-by-step explanation:
Givem the profit function
p(x) = −2000x2 + 18000x − 15000
We are to generate the price range that will generate a monthly profit of at least $25,000
Substitute into the function we have;
25000 = −2000x2 + 18000x − 15000
Divide through by 1000
25 = -2x²+18x-15
Rearrange
-2x²+18x-15-25 = 0
2x²-18x+40 = 0
Divide through by 2
x²-9x+20 = 0
Factorize
x²-5x-4x+20 = 0
x(x-5)-4(x-5) = 0
x-4 = 0 and x-5 = 0
x = 4 and x = 5
Hence the price range that will generate a monthly profit of at least $25,000 is between $4 and $5 inclusive
Subtract normally as if 32.6 is 316 and 1.9 is 19. Then you move the decimal point two places to the left of the answer
the answer is 29.7
The decay factor of the equation given in the task content is; 0.87.
<h3>What is the decay factor from the equation?</h3>
According to the task content; the equation given is; y = 453(0.87)^4.
By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.
Read more on decay factor;
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Table #1:
Using the first two points (2,1) and (5,3)
You get (x-2)/3 = (y-1)/2
But then the 3rd point (8,7) does not work, so this is not linear.
Table #2
Using the first two points (1,10) and (2,13)
You get x-1 = (y-10) /3
But then the 3rd point (3,18) does not work so this is also not linear.
Table #3
Using the first two points (2,1) and (4,6)
You get x-2 /2 = y-1 /5
And all the other points will work with this, which makes this table linear.
Rewrite the equation to get y = 5/2x-4
I'll start by expanding everything, and 10^(x) means we move the decimal x places to the right. If we move the decimal to the right but there's no number there, that number is 0.
The populations are as follows (in the order in the graph) -
127,180,000
200,000,000
80,619,000
63,708,000
173,615,000
152,510,000
The first difference is the number of digits. The more, the better. The two that stand out at the bottom are Germany and the UK. Next, we look at the leftmost number. Since 6<8, Germany's population > UK's population. All other countries are greater than Germany. Next, we look at the next smallest amount of digits, which is every other country. We look at the first number, which gives us Japan, Nigeria and Bangladesh. Next, we look at the second number, and since 2<5<7, Japan is smaller than Bangladesh and Nigeria is bigger than Bangladesh. Our current list is as follows:
United Kingdom (UK), Germany, Japan, Bangladesh, Nigeria. Since Brazil
has been proven to be greater than the rest (as it has more digits and 2>1), our list is now
United Kingdom (UK), Germany, Japan, Bangladesh, Nigeria, Brazil
