Any number inside the modulus sign becomes positive. This means
and so we have,

Solving these gives us


However if we check the second solution in the original equation we obtain
. This is false and so
can't be a solution.
Therefore the only solution is
.
(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)
If my simplification is valid the answer is:
1.4 % growth each minute
I don’t feel like the representation
P = 120(1.82) is important in this certain problem.
So P the predicted number of bacteria is not practical with this problem.
Use the 82% per hour and divide it by 60 because there are 60 minutes in an hour.
When doing this you find the rate in which bacteria grows which is about 1.4%.
The prediction is about 1.82 percent for 120 something it’s not clarified, but I’m guessing that’s minutes.
So you can prove that the prediction is over the rate in which bacteria grows per minute.
G(x) is an absolute value function. The standard form for an absolute value function is f(x) = |x|.
The slope of this is equal to -6/-4 or 3/2.
It is flipped over the x-axis, so it will have a negative value out front.
g(x) = -3/2|x| is the equation for this graph.