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1 answer:
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Answer:
Step-by-step explanation:
Given A = 5i + 11j – 2k and B = 4i + 7k, the vector projection of B unto a is expressed as
b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)
note that i.i = j.j = k.k =1
b.a = 5(4)+11(0)-2(7)
b.a = 20-14
b.a = 6
||a|| = √5²+11²+(-2)²
||a|| = √25+121+4
||a|| = √130
square both sides
||a||² = (√130)
||a||² = 130
<em>Hence the projection of b unto a is expressed as </em><em></em>
Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
For t=0, we have:
If we use the duplication time, we have:
Then, we have the model as:
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
The rate of growth can be calculated as dP/dt and is:
For t=8, the rate of growth is:
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as: