How to solve the problem
1 answer:
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Answer:
Step-by-step explanation:
The logistic equation is the following one:
In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.
In this problem, we have that:
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that .
The number of fish tripled in the first year. This means that .
Using the equation for P(1), that is, P(t) when , we find the value of r.
Applying ln to both sides.
This means that the expression for the size of the population after t years is:
Answer: 9 and 3/7
Step-by-step explanation: To multiply a mixed number by a mixed number, we first want to write each mixed number as an improper fraction.
We can write a mixed number as an improper fraction by multiplying the denominator by the whole number and adding the numerator.
We can change to the improper fraction 30/7.
We can also change to the improper fraction 11/5.
Now, we are simply multiplying fractions. To multiply fractions, we multiply across the numerators and multiply across the denominators. When we multiply these fractions, we will end up with the fraction 330/35. Since 330/35 is not in lowest terms, we need to divide both the numerator and denominator by the greatest common factor of 330 and 35 which is 5 and we will get the improper fraction 66/7.
Notice however that 66/7 can be changed into a mixed number by dividing the denominator which is 7 into the numerator which is 66.
66 divided by 7 equals 9 with a remainder of 3 so we can write 66/7 as the mixed number 9 and 3/7.
Therefore, 4 and 2/7 × 2 and 1/5 = 9 and 3/7