3 days after the start of an experiment there were 484 bacteria in a culture. After 5 days there were 1135. Use a system of equations to determine the initial number of bacteria in the culture (c) and the k value for the growth
Answers
Answer:
- c = 135
- k = 0.42615
Step-by-step explanation:
We assume you want your model to be ...
p = c·e^(kt)
Filling in (t, p) values of (3, 484) and (5, 1135), we have two equations in the two unknowns:
484 = c·e^(3k)
1135 = c·e^(5k)
Taking logs makes these linear equations:
ln(484) = ln(c) +3k
ln(1135) = ln(c) +5k
Subtracting the first equation from the second, we have ...
ln(1135) -ln(484) = 2k
k = ln(1135/484)/2 ≈ 0.42615
Using that value in the first equation, we find ...
ln(484) = ln(c) +3(ln(1135/484)/2)
ln(c) = ln(484) -(3/2)ln(1135/484)
c = e^(ln(484) -(3/2)ln(1135/484)) ≈ 134.8
The initial number in the culture was 135, and the k-value is about 0.42615.
_____
I prefer to start with the model ...
p = 484·(1135/484)^((t-3)/2)
Then the initial value is that obtained when t=0:
c = 484·(1135/484)^(-3/2) = 134.778 ≈ 135
The value of k the log of the base for exponent t. It is ...
ln((1135/484)^(1/2)) = 0.426152
This starting model matches the given numbers exactly. The transformation to c·e^(kt) requires approximations that make it difficult to match the given numbers.
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For this model, the base of the exponent is the ratio of the two given population values. The exponent is horizontally offset by the number of days for the first count, and scaled by the number of days between counts. The multiplier of the exponential term is the first count. The model can be written directly from the given data, with no computation required.
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b. Use the property b*b b to express xy in terms of b, p, and q
c. Compute log b(xy) and simplify
Answers
Answer with Step-by-step explanation:
a.
Taking both sides log
Using identity:
Using identity:
b.
We know that
Using identity
c.
Substitute the values then we get
By using
Hence,
Final answer:
To prove the property log b(xy) = log bx + log by, we let x = and y =
, express xy in terms of the base b and the exponents p and q, and then use the properties of logarithms to show the equality.
Explanation:
The student is asking to prove the logarithmic property − log b(xy) = log bx + log by. Here's a step-by-step explanation:
Let x = bp and y = bq. To solve for p and q, take the logarithm base b of both sides. Thus, p = logbx and q = logby.
Using the property of exponents, xy = bp*bq = bp+q.
Now compute logb(xy). According to the logarithmic property, logb(bp+q) = p + q. Since p = logbx and q = logby, then logb(xy) = logbx + logby.
Therefore, we have proven the given logarithmic property using the steps provided in the question.
Learn more about Logarithmic Properties here:
#SPJ3
Answers
Answer:
B. 3x + y = 4
Step-by-step explanation:
y = -3x + 4
Check:
3x + y = 4
-3x -3x
y = -3x + 4
Answer:
It is B
Step-by-step explanation:
This is because if you use the point (1,1) for example then both x and y are 1.
1 X 3 = 3 and 3 + 1 = 4.
random variable x is given in the table.
Answers
1
Step-by-step explanation:
p(x≤20)=p(x=-10) +p(x=-5)+p(X=0) +p(x=5) +p(x=10)+ p(X=15)+p(X=20)
This, p(X≤20)=0.20+0.15+0.05+0.1+0.25+0.1+0.15
=1
(7x-1)+(9x+5)
Answers
Answers
Answer: 120[4(x^6 + x^3 + x^4 + x) +7(x^7 + x^4 + x^5 + x^2)]
Step-by-step explanation:
=24x(x^2 + 1)4(x^3 + 1)5 + 42x^2(x^2 + 1)5(x^3 + 1)4
Remove the brackets first
=[(24x^3 +24x)(4x^3 + 4)]5 + [(42x^4 +42x^2)(5x^3 + 5)4]
=[(96x^6 + 96x^3 +96x^4 + 96x)5] + [(210x^7 + 210x^4 + 210x^5 + 210x^2)4]
=(480x^6 + 480x^3 + 480x^4 + 480x) + (840x^7 + 840x^4 + 840x^5 + 840x^2)
Then the common:
=[480(x^6 + x^3 + x^4 + x) + 840(x^7 + x^4 + x^5 + x^2)]
=120[4(x^6 + x^3 + x^4 + x) +7(x^7 + x^4 + x^5 + x^2)]
Answers
it's simple
3t+3
just this