Answer:
7.5
Step-by-step explanation:
Answer:
(-1,-5)
Step-by-step explanation:
Solve by substitution
Sin = - 4/8
Quadrant IV = only cosine is positive
a = height (4)
b = base ( 8^2-4^2=b^2
b = 6.93 @
c = hypothenuse(8)
cos =
/8
tan = - 4/
sec = 1/cos
1/cos = 1/ (
/8)
sec = 8/
csc = 1/sin
1/sin = 1/(-4/8)
csc = - 2
cot = 1/tan
1/tan = 1/(-4/
)
cot = -
/4
The equation to be solved is: 3 [ 2 ^ (2t - 5) ] - 4 = 10
The steps are:
1) transpose - 4=> 3 [ 2^ (2t - 5) ] = 10 + 4
2) Combine like terms => 3 [2^ (2t - 5) ] = 14
3) Divide both terms by 3 => 2^ (2t - 5) = 14 / 3
4) Take logarithms of both sides => (2t - 5) log (2) = log (14/3)
5) Divide both sides by log (2) =>
log (14/3)
2t - 5 = -------------------
log (2)
6) transpose - 5+>
log (14/3)
2t = ------------------- + 5 = 2.22 + 5
log (2)
2t = 7.22
7) divide both sides by 2 => t = 7.22 / 2 = 3.61
Don't know whether or not you've encountered differential equations yet, but will try that approach here.
The growth rate is dy/dt = ky (which states that the rate is proportional to the size of the population, y, and k is a constant.
Grouping like terms,
dy
--- = kt, so y = Ne^kt
y
We are told that at t=0, there are 880 bacteria. Thus, 880=N. Therefore,
y = 880e^(kt). After 5 hours the pop will be 4400; using this info, find k:
4400=880e^(5k), or 5 = e^(5k). So, our y = 880e^(kt) becomes
y = 880e^(5t).
What will be the pop after 2 hours? y(2)=880e^(10) = 880(22026) =
approx. 19,383,290 bacteria
Time to reach a pop of 2550? 2550 = 880e^(5t). Find t.
ln 2550 = ln 880 + 5t, so ln 2550 - ln 880 = 5t. Divide both sides by 5 to obtain this time, t.
