Can you help me with 7 and 8
1 answer:
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Answer:
a)
b) 54.225 square centimeters.
c) 2.52 hours
Step-by-step explanation:
The population growth law is:
In which P(t) is the population after t hours, is the initial population and r is the growth rate, as a decimal.
In this problem, we have that:
The colony occupied 2 square centimeters initially, so
The colony triples every 4 hours. So
(a) An expression for the size P(t) of the colony at any time t.
We have to find the value of r. We can do this by using the P(4) equation.
Applying ln to both sides, we get:
So
(b) The area occupied by the colony after 12 hours.
(c) The doubling time for the colony?
t when .
Applying ln to both sides
Answer:
C
Step-by-step explanation:
We want to simplify the rational expression:
First, we can factor both the numerator and the denominator. This yields:
Cancel like terms:
However, since we canceled a term from our expression, we must place restrictions in order to stay true to the original expression.
Rational expressions are undefined whenever the denominator equals 0. The denominator is (before canceling):
Solve for n. By the zero product property:
Therefore:
By taking the square root of both sides (since we are taking an even root, it is required to have plus/minus):
Therefore, our fully simplified expression is:
Hence, our answer is C!