Answer: 100*(1.032)^t which can be written as 
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Explanation:
b = value of cup after t years
t = time in years (eg: t = 2 means 2 years have passed by)
The value starts at b = 100. After year 1, the value jumps up by 3.2% so we multiply the value $100 by 1.032 which is the proper multiplier to help increase by 3.2%; to see this, notice how 100% + 3.2% = 1 + 0.032 = 1.032
After 2 years, the value jumps another 3.2% so we have another copy of 1.032 multiplied. Then for 3 years, we'll have 3 copies of 1.032 multiplied. And so on.
For t years, we'll have t copies of 1.032 as the multiplier. So we will multiply the initial value 100 by (1.032)^t
That is why the equation is
b = 100*(1.032)^t
which can be written as
![\bf \lim\limits_{x\to \infty}~\left( \cfrac{1}{8} \right)^x\implies \lim\limits_{x\to \infty}~\cfrac{1^x}{8^x}\\\\[-0.35em] ~\dotfill\\\\ \stackrel{x = 10}{\cfrac{1^{10}}{8^{10}}}\implies \cfrac{1}{8^{10}}~~,~~ \stackrel{x = 1000}{\cfrac{1^{1000}}{8^{1000}}}\implies \cfrac{1}{8^{1000}}~~,~~ \stackrel{x = 100000000}{\cfrac{1^{100000000}}{8^{100000000}}}\implies \cfrac{1}{8^{100000000}}~~,~~ ...](https://tex.z-dn.net/?f=%5Cbf%20%5Clim%5Climits_%7Bx%5Cto%20%5Cinfty%7D~%5Cleft%28%20%5Ccfrac%7B1%7D%7B8%7D%20%5Cright%29%5Ex%5Cimplies%20%5Clim%5Climits_%7Bx%5Cto%20%5Cinfty%7D~%5Ccfrac%7B1%5Ex%7D%7B8%5Ex%7D%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7Bx%20%3D%2010%7D%7B%5Ccfrac%7B1%5E%7B10%7D%7D%7B8%5E%7B10%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B10%7D%7D~~%2C~~%20%5Cstackrel%7Bx%20%3D%201000%7D%7B%5Ccfrac%7B1%5E%7B1000%7D%7D%7B8%5E%7B1000%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B1000%7D%7D~~%2C~~%20%5Cstackrel%7Bx%20%3D%20100000000%7D%7B%5Ccfrac%7B1%5E%7B100000000%7D%7D%7B8%5E%7B100000000%7D%7D%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B8%5E%7B100000000%7D%7D~~%2C~~%20...)
now, if we look at the values as "x" races fast towards ∞, we can as you see above, use the values of 10, 1000, 100000000 and so on, as the value above oddly enough remains at 1, it could have been smaller but it's constantly 1 in this case, the value at the bottom is ever becoming a larger and larger denominator.
let's recall that the larger the denominator, the smaller the fraction, so the expression is ever going towards a tiny and tinier and really tinier fraction, a fraction that is ever approaching 0.
Answer:
Population of bacteria four hours later 
or nearest whole number
Step-by-step explanation:
Given,
Let amount of bacteria four hours later is=A
Rate of increase of bacteria per hour 
Initial population of bacteria is =54
Time 4 hours
Find the population of bacteria 4 hours later
Solution,
![\left [ x \right ]_{54}^{A}=4.0565/1.3\left [e^{1.3t} \right ]_{0}^{4}](https://tex.z-dn.net/?f=%5Cleft%20%5B%20x%20%5Cright%20%5D_%7B54%7D%5E%7BA%7D%3D4.0565%2F1.3%5Cleft%20%5Be%5E%7B1.3t%7D%20%20%5Cright%20%5D_%7B0%7D%5E%7B4%7D)
Population of bacteria 4 hours later is
Answer:
Im pretty sure it is B
Step-by-step explanation:
at first I said D but then I realized it said positive
Answer:
The answer is the red square, 2* pi* r
Step-by-step explanation:
In order to find the circumference* of a circle, you need the radius to be multiplied with pi and 2
