A.) P(t) = P0exp(kt)
P(20/60) = 40 exp(20k/60)
80 = 40 exp(k/3)
exp(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = exp(8k) = exp(8(3ln(2)) = exp(24ln(2)) = exp(16.6355) = 16777216 cells / hour
e.) P(t) = 40(2)^3t; t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
First of all, we can observe that
So the expression becomes
This means that the expression is defined for every 
Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask
Since we can't accept 3 as an answer, the actual solution set is
![(-\infty,-2] \cup [2,3) \cup (3,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C-2%5D%20%5Ccup%20%5B2%2C3%29%20%5Ccup%20%283%2C%5Cinfty%29)
It would take 20 hours since 8,000 times 5 is 40,000 so 4 times 5 is 20.
Logic.
9514 1404 393
Answer:
- $0.04 per cubic foot
- c(w) = 0.04w +80
- 3400 cubic feet
Step-by-step explanation:
(a, b) We are given two pairs of values:
(w, c) = (1900, 156) and (2600, 184)
so we can write the equation of the relationship using the 2-point form of the equation of a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
c = (184 -156)/(2600 -1900)(w -1900) +156 . . . . . substitute given points
c = 28/700(w -1900) +156
c(w) = 0.04w +80
The charge per cubic foot is $0.04.
__
(c) For a bill of $216, the amount of water used is ...
216 = 0.04w +80
136 = 0.04w
3400 = w
Use of 3400 cubic feet of water would lead to a bill of $216.
Answer:
3 minutes: 792
30 minutes: 7920
Step-by-step explanation:
Since 264 parts are made in one minute you can multiply 264 with 3 for 3 minutes:
264 times 3 is 792
For 30 minutes, we can multiply 264 with 30:
264 times 30 is 7920
Hope this helps!
