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Schach [20]
3 years ago
12

A marine biologist monitors the population of sunfish in a small lake. He records 800 sunfish in his first year, 600 sunfish in

his fourth year, 450 sunfish in his sixth year, and 350 sunfish in his tenth year. Using the exponential regression equation (rounded to the hundredths),
1. Predict when the population of sunfish in the lake will be 200.

2. Predict the number of sunfish in the lake in the 25 thyear.
Mathematics
1 answer:
Colt1911 [192]3 years ago
7 0

Answer:

Let's use the variable y to represent the number of years passed since the first year.

The population on the first year (y = 0) was 800

The population in the second year (y = 1) was 600.

The ratio in which the population decreased can be calculated as:

R = 600/800 = 0.75

This means that 600 is the 75% of 800, this also means that between the first year and the second year, the population decreased by the 25%

Now let's look at the ratio between the second and third year (y = 2), the population the third year was 450

Now the ratio is:

R = 450/600 = 0.75

Same as before, then we already can see that the population will decrease by 25% each year.

The generic exponential decay equation is:

f(y) = A*(1  - r)^y

where:

A = initial population, in this case, is 800

y = our variable, in this case, represents the number of years

r = the amount that decreases per each unit of our variable, this must be written in decimal form. In this case, we know that the population decreases by 25% each year, and 25% written in decimal form is 0.25

Also, (1 - r) = R, where R is the ratio we found earlier.

To do this, we just divide 25% by 100% to get (25%/100% = 0.25)

Then our equation will be:

f(y) = 800*(1 - 0.25)^y

f(y) = 800*( 0.75)^y

1) We want to predict when the population will be 200.

to do this, we set:

f(y) = 200 = 800*( 0.75)^y

and solve it for y.

(200/800) = 0.75^y

(1/4) = 0.75^y

Now we can use the relationship:

Ln(a^x) = x*ln(a)

Then let's apply Ln( ) in both sides to get

ln(1/4) = y*ln(0.75)

ln(1/4)/ln(0.75) = y = 4.8 years.

This means that 4.8 years after the first year, the population will be around 200.

2) The population in the 25 th year (this is 24 years after the first one, so we take y = 24) is:

f(24) = 800*(0.75)^(24) = 0.80

Around this point, we will have no more sunfish in the lake.

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4 0
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Y_Kistochka [10]

<em>Answer:</em>

<em>2</em>

<em>Step-by-step explanation:</em>

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3 years ago
on Monday it rained 1 3/4 of an inch and on Tuesday it rained 2 2/3 of an inch. how many inches did it rain altogether?​
iogann1982 [59]

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8 0
3 years ago
It takes 1 hour (t) to fill the water tank of volume (V) 750 m3. Identify the dependent and the independent variables.
Natalija [7]

Answer:

The time t is the independent variable while the volume V is the dependent variable

Step-by-step explanation:

A variable is a parameter that changes.

We have two types namely dependent and independent variables.

A dependent variable is a variable which its value needs to be determined based on the value of another variable while and independent variable is a variable which its value independent of other parameters.

In our question, It takes 1 hour (t) to fill the water tank of volume (V) 750 m3.

The volume of the tank V changes as time changes. So the volume of the tank V is dependent on time, t.  

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Since the volume of the tank is the variable that needs to be determined based on another variable-which is time,t- it is the dependent variable, while the time,t is the independent variable since its value is not determined based on other parameters.

4 0
2 years ago
274,635 rounded to the nearest thousands
Firlakuza [10]

275000 is your answer

hope it help

6 0
2 years ago
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