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svlad2 [7]
2 years ago
5

Find the product.

Mathematics
2 answers:
notsponge [240]2 years ago
8 0

Answer:

A) 4n²- 4

Step-by-step explanation:

use the FOIL method:

F = first, meaning multiply the 1st terms in each factor

O = outer, meaning multiply the 1st term in first factor and last term in second

I = inner, meaning multiply the 2nd term in first factor and 1st term in second

L = last, meaning multiply the last terms in each factor

F = 2n · 2n = 4n²

O = 2n(-2) = -4n

I = 2(2n) = 4n

L = 2(-2) = -4

you have 4n² - 4n + 4n - 4

this can be simplified by adding the two middle terms (which will zero out):

4n²- 4

Harrizon [31]2 years ago
5 0

(2n+2)(2n-2)\\\\=(2n)^2 -2^2 ~~~~~~;[a^2 -b^2 =(a-b)(a+b)]\\\\=4n^2 -4

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A marine biologist monitors the population of sunfish in a small lake. He records 800 sunfish in his first year, 600 sunfish in
Colt1911 [192]

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

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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

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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)

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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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