Answer:

Step-by-step explanation:
So, the function, P(t), represents the number of cells after t hours.
This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.
C)
So, we are given that the quadratic curve of the trend is the function:

To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:
![\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5BP%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2-9.28t%2B16.43%5D)
Expand:
![P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]](https://tex.z-dn.net/?f=P%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B-9.28t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B16.43%5D)
Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:
![P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]](https://tex.z-dn.net/?f=P%27%28t%29%3D6.10%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D-9.28%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5D)
Differentiate. Use the power rule:

Simplify:

So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:

Multiply:

Subtract:

This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.
And we're done!
Divide 5 by 2 representing each box by the price. Which equals to $2.50 each box.
Answer:
y=-1/4x
Step-by-step explanation:
METHOD 1: The basic slope-intercept equation is <em>y=ax+b</em>. To achieve the slope with two points, this is the equation:

All you have to do is insert points (-4, 1) and (4, -1) into their corresponding locations.

With this equation, you will be able to find the slope. Then you can simply graph it to connect the two dots.
METHOD 2: Simply connect the two dots with a straight line (use a ruler or something with a straight edge.) Then count how many spaces up/down and left/right. If the line goes from top to bottom from left to right, it is a negative slope (hence, the -1/4.)
Answer:
C) 1
F) 29
Step-by-step explanation:
all numbers less than 30 are solutions
10.2 ft Ans.
We solve this using geometric series.
A1 = 12 ft
A2 = ?
A3 = 8.67ft
Now, for geomteric progression,


A2 = 10.2 ft