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Given the data shown below, which of the following is the best prediction for

Soloha48 [4]

Answer:

The best prediction for the number of years it will take for the population to reach 200,000 is 9.41

Step-by-step explanation:

Year Population

1 11,920

2 16,800

3 23,300

4 33,000

5 45,750

6 64,000

$y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)$

Substitute the values

$11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2$

Divide 1 and 2

$\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238$

The exponential function that passes through the points (1, 11920) and (2, 16800) is $y=8457.5238 e^{0.3432t}$

Now we are supposed to find the best prediction for the number of years it will take for the population to reach 200,000

$200000=8457.5238 e^{0.3432t}$

$\frac{200000}{8457.5238}=e^{0.3432t}$

$ln(\frac{200000}{8457.5238})=0.3432t$

t = 9.41

Hence the best prediction for the number of years it will take for the population to reach 200,000 is 9.41

6 0

4 years ago

Kai pen for Ruth’s dog is 7 feet long and 6/1.3 feet wide. Her friend Ralph’s dog pen is 14 feet long and 6/1.2 feet wide. How m

rusak2 [61]

Answer:

The area of Ralph's dog pen is 2.05 times larger than the area of Ruth's dog pen.

Step-by-step explanation:

Given that the dog pen for Ruth's dog is 7 feet long and 6 / 1.3 feet wide, while her friend Ralph's dog pen is 14 feet long and 6 / 1.2 feet wide, to determine how many times larger is the area of Ralph's dog pen, the following calculation must be performed:

1/3 = 0.333

1/2 = 0.5

7 x 6.333 = X

44,333 = X

14 x 6.5 = X

91 = X

44,333 = 100

91 = X

91 x 100 / 44.333 = X

9,100 / 44,333 = X

205.26 = X

100 = 1

205.26 = X

205.26 / 100 = X

2.05 = X

Thus, the area of Ralph's dog pen is 2.05 times larger than the area of Ruth's dog pen.

4 0

3 years ago

Multiply (2.5x10^-10) (7x10^-6)

serious [3.7K]

We want to multiply $2.5\cdot10^{-10}$ by $7\cdot10^{-6}$ .

The numbers are written in scientific notation. So we expect the answer also to be in scientific notation.

the multiplication of the 10's, using the exponents rule is :

$10^{-10}\cdot 10^{-6}=10^{-10+(-6)}=10^{-10-6}=10^{-16}$

the multiplication of the other 2 numbers is:

$2.5\cdot7=17.5=1.75\cdot10$

(we write the number so that it has only one digit to the left of the decimal point).

Thus,

$(2.5\cdot10^{-10})\cdot(7\cdot10^{-6})=1.75\cdot10\cdot10^{-16}=1.75\cdot10^{-15}$

Answer: $1.75\cdot10^{-15}$

6 0

4 years ago

Read 2 more answers

Ivan has 15 yd of green felt and 12 yd of blue felt to make 3 quilt if I have I even uses the same total numbers of each of yd f

laiz [17]

Answer:

9 yards of each quilt.

Step-by-step explanation:

Let the length of each quilt be 'x'.

Given:

Length of green felt = 15 yards

Length of blue felt = 12 yards