Okay, the equation would be 12 - 2x = 8(x + 4), you got close!
what i would do first is distribute to get rid of those evil parenthesis and make this all simple ^-^
So, we take 8 times x, and 8 times 4.
Our equation, is now 12 - 2x = 8x + 32
Now, what i would do, is simplify it. Get x to one side, and a whole number to the other. Well, for me it would be easier to keep the larger number on the right, and x on the left!
So we have to be fair, and keep it equal! So, i would start with.... subtracting 32. Since its a positive 32, to cancel it out we have to subtract 32, to get to zero! so, by subtracting 32 on both sides ( 12 - 32 and 32 - 32) we end up with -20 - 2x = 8x
Now looking at - 20 - 2x = 8x, i can see what i need to do. i need to get x to one side, and whole numbers to the other. There are no whole numbers on the right, just variables and coefficients, so i have to get that x away from the left!
So, im going to add 2x on both sides, to eliminate it! So we add 2x on the left to cancel it out, and add 2 x on the right to balance it out! We are now left with -20 = 10x
Now what we do is we get rid of that tag along right by the x! Yep, that little 10 there! He has to go!
How to we get rid of him? Well, he is being multiplied by the x! So, we have to do the opposite and divide to get him alone. So, we divide by 10 on both sides, and we are left with -2 = x!
Now, time to check your answer! Basically, you replace x with -2 in the equation! Here we go:
12 - 2(-2) = 8(-2 + 4)
First we should start with multiplying! when we multiply the -2 in the equation, we get 12 + 4 = 8(2), and we can finish that off by simplifying it to 12 + 4 = 16
when we simplify it and add 12 + 4, we get 16. So we are left with 16 = 16.
This equation is true, so we are right! -2 DOES equal x!
a) growth will reach a peak and begin declining after about 42.6 days. 5000 people will be infected at that point
b) the infected an uninfected populations will be the same after about 42.6 days
Step-by-step explanation:
We have assumed you intend the function to match the form of a logistic function:
This function is symmetrical about its point of inflection, when half the population is infected. That is, up to that point, it is concave upward, increasing at an increasing rate. After that point, it is concave downward, decreasing at a decreasing rate.
a) The growth rate starts to decline at the point of inflection, when half the population is infected. That time is about 42.6 days after the start of the infection. 5000 people will be infected at that point
b) The infected and uninfected populations will be equal about 42.6 days after the start of the infection.
