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3 years ago

Please help me out I don’t understand I’ll give more if right

Mathematics

1 answer:

aksik [14]3 years ago

7 0

Answer:

x = 15.

Step-by-step explanation:

We apply the tangent-secant theorem:

18^2 = 12(12+x)

324 = 144 + 12x

12x = 324 - 144 = 180

x = 180/12 = 15.

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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]

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.

7 0

3 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

lbvjy [14]

Answer:

Step-by-step explanation:

6 0

3 years ago

Indicate whether the following statement is true or false: An exponential growth function eventually exceeds a quadratic functio

Mila [183]

The given statement is true.

In general, the growth rate of exponential functions is far greater than the quadratic function. This can be illustrated through an example.

Consider an exponential function $2^{x}$ and a quadratic function $200 x^{2} +150x+500$ .

Note that the leading coefficient of the quadratic function is far greater than the base of the exponential function but still the exponential function will exceeds the quadratic function after x = 15.664 as shown in the graph below.

Therefore, we can conclude that the given statement is correct.