Step-by-step explanation:

Answer: A. 
B. A'(5) = 1.76 cm/s
Step-by-step explanation: <u>Rate</u> <u>of</u> <u>change</u> measures the slope of a curve at a certain instant, therefore, rate is the derivative.
A. Area of a circle is given by

So to find the rate of the area:


Using 

Then
![\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D2.%5Cpi.r.%5B%5Cfrac%7B726%7D%7B%28t%2B11%29%5E%7B3%7D%7D%5D)
![\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%3D2.%5Cpi.%5B3-%5Cfrac%7B363%7D%7B%28t%2B11%29%5E%7B2%7D%7D%5D.%5Cfrac%7B726%7D%7B%28t%2B11%29%5E%7B3%7D%7D)
Multipying and simplifying:

The rate at which the area is increasing is given by expression
.
B. At t = 5, rate is:




At 5 seconds, the area is expanded at a rate of 1.76 cm/s.
<span>p=210e^(0.0069*20)
'e' is a mathematical constant equal to 2.718281828459
</span>
<span>0.0069*20 = .138
e^.138 =
</span>
<span>2.718281828459^.138 =
</span>
<span>
<span>
<span>
1.1479755503
</span>
</span>
</span>
210 * <span>1.1479755503 =
</span>
<span>
<span>
<span>
241.074865563
</span>
</span>
</span>
There are a lot of fraction that can be equal to the values given above. It can be as follows:
<span>1/5 = 2/10, 3/15, 4/20, 5/25, 6/30, 7/35, 8/40
4/7 = 8/14, 12/21, 16/28
6/30 = 12/60, 18/90, 24/120
5/15 = 1/3 , 10/30, 20/60
Hope this helps. Have a nice day.</span>