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A country's population in 1993 was 94 million. in 1999 in was 99 million. estimate the population in 2005 using the exponential

Jet001 [13]

The initial population is
P₀ = 94 million in 1993

The growth formula is
$P(t) = P_{0}e^{kt}$
where P(t) is the population (in millions) after t years, measured from 1993.
k = constant.

Because P(5) = 99 million (in 1999),
$94e^{5k} = 99 \\e^{5k}=1.0532 \\ 5k = ln(1.0532) \\ k = 0.010367$

In the year 2005, t = 12 years, and
$P(12)=94e^{0.010367*12} = 106.45$

Answer: 106 million (nearest million)

7 0

2 years ago

The diagram represents a difference of squares. A 2-column table with 2 rows. The labels for the columns and rows are blank. Fir

olga55 [171]

I think its fisrts one

8 0

2 years ago

Read 2 more answers

Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 t

andreyandreev [35.5K]

Answer:

How far should he ride on each of the four days to reach his goal?

1st day: $8$ miles

2nd day: $12$ miles

3rd day: $18$ miles

4th day: $27$ miles

Step-by-step explanation: As the problem says, $x$ is the number of miles he rides on the first day. Let's start off with that.

1st day: $x$ miles

He want to ride 1.5 times as far as he rode the day before... no 1.5 more, but 1.5 times as far as he rode the day before; you would multiply 1.5 with the previous day's length.

2nd day: $1.5x$

Then you multiply $1.5$ to $1.5x$ to get the third day's.

3rd day: $2.25x$

4th day: $3.375x$

----------------------------

Phew! Gavin wants to ride a total of 65 miles over these four days, so if Gavin added all the miles of the four days, he should get 65...

1st+2nd+3rd+4th=65

$x+1.5x+2.25x+3.375x=65$

$8.125x=65$

$\frac{8.125x}{8.125}=\frac{65}{8.125}$

$x=8$

Yes! Now that we've got the hard part done... substitute 8 for ever single $x$ .

1st day: $8$ miles

2nd day: $1.5(8)=12$ miles

3rd day: $2.25(8)=18$ miles

4th day: $3.375(8)=27$ miles

-------------------------

Checking my answer:

Just add the miles!

$8+12+18+27=65$

$65=65$

✓

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Hope that helps! :D

5 0

2 years ago

The graph of f(x) = StartRoot x EndRoot is reflected over the y-axis. Use the graphing calculator to graph this reflection. Whic

labwork [276]

Answer:

(–81, 9), (–36, 6), (–1, 1) are the correct three points.

Step-by-step explanation:

Given the function:

$f(x) =\sqrt x$

Please refer to the attached image.

The green line shows the graph of actual function.

It is reflected over y axis.

The reflected graph is shown in black color in attached image.

When reflected over y axis, the sign of variable $x$ changes from Positive to Negative.

So, the resultant function becomes:

$f(x)=\sqrt{-x}$

i.e. we will have to give the values of x as negative now.

so, the options in which value of x is negative are the possible answers only.

The possible answers are:

(–81, 9), (–36, 6), (–1, 1) and

(–49, 7), (–18, 9), (–1, 1)

Now, we will check the square root function condition.

In the 2nd option, (–18, 9) does not satisfy the condition.

So, the correct answer is:

(–81, 9), (–36, 6), (–1, 1)

7 0

2 years ago

In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.

pshichka [43]

Answer:

The answer is:

$\bold{c\approx 20.2\ units}$

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

$cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Putting all the values.

$cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units$

The answer is:

$\bold{c\approx 20.2\ units}$

4 0

2 years ago