Which choices are common factors of the numerator and denominator of 18/24

Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species

kotegsom [21]

Answer:

$P(t) = \frac{160000e^{1.36t}}{2000 + 80(e^{1.36t} - 1)}$

Step-by-step explanation:

The logistic equation is the following one:

$P(t) = \frac{KP(0)e^{rt}}{K + P(0)(e^{rt} - 1)}$

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 $P(0) = 80, K = 2000$ .

The number of fish tripled in the first year. This means that $P(1) = 3P(0) = 3(80) = 240$ .

Using the equation for P(1), that is, P(t) when $t = 1$ , we find the value of r.

$P(t) = \frac{KP(0)e^{rt}}{K + P(0)(e^{rt} - 1)}$

$240 = \frac{2000*80e^{r}}{2000 + 80(e^{r} - 1)}$

$280*(2000 + 80(e^{r} - 1)) = 160000e^{r}$

$280*(2000 + 80e^{r} - 80) = 160000e^{r}$

$280*(1920 + 80e^{r}) = 160000e^{r}$

$537600 + 22400e^{r} = 160000e^{r}$

$137600e^{r} = 537600$

$e^{r} = \frac{537600}{137600}$

$e^{r} = 3.91$

Applying ln to both sides.

$\ln{e^{r}} = \ln{3.91}$

$r = 1.36$

This means that the expression for the size of the population after t years is:

$P(t) = \frac{160000e^{1.36t}}{2000 + 80(e^{1.36t} - 1)}$

4 0

3 years ago

I REALLY NEED SOME HELP! PLEASE GUYS I WILL DO ANYTHING! BRAINLIEST!

denis-greek [22]

I’m pretty sure the answer is d or c

5 0

3 years ago

Suppose a student started with 139.0 mg of trans-cinnamic acid, 463 mg of pyridinium tribromide, and 2.45 mL of glacial acetic a

Sliva [168]

Answer:

0.2889 g brominated product

64.6 %

Step-by-step explanation:

This is a bromination chemical reaction of an alkene and we are asked to calculate the theoretical and percent yield. Thus to solve it we have to perform a calculation based on the balanced chemical reaction.

The pyridinium tribromide is used as a generator of molecular bromine in situ, and bromine will add to the double bond in trans-cinnamic acid so we know the reaction occur in a one to one mole fashion.

trans-cinnamic acid + pyridinium tribromide ⇒ 2,3-dibromo-3-

phenylpropanoic acid

Molar weight trans-cinnamic acid = 148.16 g/mol

mass trans-cinnamic acid = 139.0 mg x 1g/1000 mg = 0.139 g

# mol trans-cinnamic acid = 0.139 g / 148 g/mol = 9.38 x 10⁻⁴ mol

Since our reaction is 1 mol trans-cinnamic acid produces 1 mol 2,3-dibromo-3-phenylpropanoic acid, it follows that the theoretical yield is:

1 mol 2,3-dibromo-3-phenylpropanoic acid / trans-cinnamic acid x 9.38 x 10⁻⁴ mol trans-cinnamic acid

= 9.38 x 10⁻⁴ mol 2,3-dibromo-3-phenylpropanoic acid

In grams the the theoretical yield is:

molar mass 2,3-dibromo-3-phenylpropanoic acid = 307.97 g/mol

The theoretical mass 2,3-dibromo-3-phenylpropanoic acid:

= 9.38 x 10⁻⁴ mol 2,3-dibromo-3-phenylpropanoic acid x 307.97 g/mol

= 0.2889 g

% yield = mass experimental/mass theoretical

= 0.1866 g / 0.2889 g x 100 = 64.6 %

4 0

3 years ago

Which statements are true about mean absolute deviation? Select all that apply. The mean absolute deviation is impacted by outli

Paul [167]

The answer is A,C,E on ed2020

4 0

3 years ago

Read 2 more answers

Liam needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.

Luden [163]

Answer:

$767.25 - $111 = $656.25

$656.25 ÷ 5.25 = $125

7 0

3 years ago