Classify the equilibrium solutions as asymptotically stable or unstable. Entry field with incorrect answer is unstable, is unsta
1 answer:
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Answer:
Part a) The number is 8
Part b) The initial number of bacteria is 4
Part c)
Part d)
Step-by-step explanation:
we know that
The equation of a exponential function is equal to
where
y is the number of bacteria
x is the time in hours
b is the base of the exponential function
a is the initial number of bacteria
Part a) When comparing the "# of Bacteria" each hour, what is the number being multiplied by each time?
we know that
For x=1 h ----> y=32 bacteria
For x=2 h ----> y=256 bacteria
For x=3 h ----> y=2,048 bacteria
For x=4 h ----> y=16,384 bacteria
For x=5 h ----> y=131,072 bacteria
For x=6 h ----> y=1,048,576 bacteria
so
256/32=8
2,048/256=8
16,384\2,048=8
131,072/16,384=8
1,048,576\131,072=8
so
the base of the exponential function b is 8
Part b) What is the initial number of bacteria? (at time zero)
we know that
The number of bacteria at time x=1 hour , divided by the number of bacteria at time x=0 must be equal to 8 (see part a)
so
solve for a
Part c) Write a rule for this table
we have
we have
substitute
Part d) Suppose you started with 100 bacteria, but they still grew by the same growth factor. Write the function rule for this situation
In this case
---> the growth factor is the same
so
The right answer is C. never
The quotient of two algebraic expressions is a<em> fractional expression. </em> Moreover, the quotient of two <em>polynomials</em> such as:
is called a rational expression. So according to this definition rational expressions does not contain logarithmic functions. In fact, a rational expression is an expression that is the ratio of two polynomials like this: