What is 8t^5 times 8t^5?

1. The number of rabbits on an island is increasing exponentially.

Zina [86]

Answer:

There are approximately 114 rabbits in the year 10

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

$50=P_o(1+r)^1$

$50=P_o(1+r)\qquad\qquad[1]$

$72=P_o(1+r)^5\qquad\qquad[2]$

Dividing [2] by [1]:

$\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}$

Solving for r:

$\displaystyle r=\sqrt[4]{\frac{72}{50}}-1$

Calculating:

r=0.095445

From [1], solve for Po:

$\displaystyle P_o=\frac{72}{(1+r)^5}$

$\displaystyle P_o=\frac{72}{(1.095445)^5}$

$P_o=45.64355$

The model can be written now as:

$P=45.64355(1.095445)^t$

In year t=10, the population of rabbits is:

$P=45.64355(1.095445)^{10}$

P = 113.6

$P\approx 114$

There are approximately 114 rabbits in the year 10

5 0

3 years ago

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i? f(x) = x2 – 2x + 2 f(x) = x3 – x

konstantin123 [22]

Answer:

$f(x)=x^{3}-3x^{2} +4x-2$

Step-by-step explanation:

we know that

The conjugate root theorem states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

In this problem we have that

The polynomial has roots 1 and (1+i)

so

by the conjugate root theorem

(1-i) is also a root of the polynomial

therefore

The lowest degree of the polynomial is 3

so

$f(x)=a(x-1)(x-(1+i))(x-(1-i))$

Remember that

The leading coefficient is 1

so

a=1

$f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2$

5 0

3 years ago

Read 2 more answers

g A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with

rodikova [14]

Answer:

a) 85.31%

b) 56 minutes

c) 17 days

d) 0.1721

Step-by-step explanation:

In order to make the calculations easier, let's standardize the curve by doing the change

$Z=\frac{X-\mu}{\sigma}$

where $\mu$ is the average trip-time and $\sigma$ the standard deviation and

P(X≤ t) is the probability that the trip takes less than t minutes.

a)

Here we are looking for the value of P(X>20).

For X=20 we have Z = (20-24)/3.8 = -1.05

So, we want the area under the standard normal curve for Z > -1.05

that we can compute either using a table or a computer and we find this area equals 0.8531

So, he arrives late to work 85.31% of the times.

(See picture 1 attached)

b)

In this case we are looking for a value t of time such that

P(X≥ t) = 20% = 0.2

So, we are seeking a value Z such that the area under the normal curve to the left of Z equals 0.2

By using a table or a computer we find Z = 0.842

(See picture 2 attached)

By inserting this value in the equation on standardization

$0.842=\frac{X-24}{38}\Rightarrow X=38*0.842+24=55.996$

So 20% of the longest trips takes 55.996 ≅ 56 minutes

c)

Since the average of days he arrives late is 85.31%, it is expected that in 20 work days he arrives late 85.31% of 20, which equals 17 days.

d)

Since the probability that he does not arrive late is 1-0.8531 = 0.1469 and the probability of arriving early is independent of the previous trip,

the probability of arriving early n days in a row is

0.1496*0.1496*...*0.1496 n times and

the probability of being early most than 10 trips in 20 days is

$(0.1469)+(0.1469)^2+(0.1469)^3+...+(0.1469)^10=0.1721$

3 0

3 years ago

On a recent day a Euro was equal to about 1.2 American dollars. Write an expression which estimates the number of dollars in x E

JulsSmile [24]

Answer:

d = 1.2e

30 dollars

Step-by-step explanation:

To write an expression, define the variables. E will be the number of euros and d will be dollars.

"Euro was equal to about 1.2 American dollars" is one euro equals 1.2 and two euros equals 2.4. So the expression is d = 1.2e.

This means if I have 1 euro, I have 1.2*1 = 1.2 dollars. If I have 2 euros, I have 1.2*2 = 2.4 dollars.

If I have 25 euros then d = 1.2*25 = 30 dollars.

4 0

4 years ago

A taxi cab driver charges $41 for a cab ride. the driver charges $8 as an initial rate and $3 per 0.5 miles. how many miles did

nadya68 [22]

He drove 66 miles. Hope that helps.

7 0

3 years ago