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Natasha2012 [34]
3 years ago
9

A country's population in 1990 was 48 million. In 1997 it was 51 million. Estimate the population in 2017 using the exponential

growth formula. Round your answer to the nearest million.
Mathematics
1 answer:
Lelechka [254]3 years ago
7 0
Hi there
First find the growth rate between 1990 and 1997
The formula is
P=Ae^rt
P 51 million
A 48 million
E constant
R growth rate?
T time 1,997−1,990=7 years
We need to solve for r
R=[log (p/A)÷log (e)]÷t
R=(log(51÷48)÷log(e))÷7
R=0.009

Now find the population in 2017
P=Ae^rt
P ?
A 48 million
R 0.009
T time 2,017−1,990=27 years
So
P=48×e^(0.009×27)
P=61 million

Hope it helps
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If a production line produces 50 mouse traps every 30 minutes over the course of a 10 hour work day with a half-hour break for l
kaheart [24]
The factory made 950 mousetraps
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3 years ago
 In a​ company, 80​% of the workers are women. If 480 men work for the​ company, how many workers are there in​ all? Use pencil
nekit [7.7K]

Answer:

The total workers are<u> 2400.</u>

Step-by-step explanation:

Given:

In company 80% of the workers are women.

480 workers are men.

Now, to find the total workers in all.

<u><em>In first way:</em></u>

If women are 80%, then men would be 100-80 = 20%.

Let the total workers be x.

According to question:

20\%\ of \ x=480

⇒\frac{20}{100} \times x=480

⇒0.20\times x=480

⇒0.20x=480

Dividing both sides by 0.20 we get:

⇒x=2400.

Total workers = 2400.

<em><u>Now, in second way</u></em>.

Again, let the total workers be  x.

According to question:

x-80\%\ of\ x=480

⇒x-\frac{80}{100}\times x=480

<em>On solving:</em>

⇒x-0.80x=480

⇒0.20x=480

<em>Dividing both sides by 0.20 we get:</em>

⇒x=2400.

<em>Total workers = 2400.</em>

Therefore, the total workers are <u>2400</u>.

7 0
3 years ago
-/2 points
Rom4ik [11]

Answer:

Part 1) The domain of the quadratic function is the interval  (-∞,∞)

Part 2) The range is the interval  (-∞,1]

Step-by-step explanation:

we have

f(x)=-x^2+14x-48

This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)

step 1

Find the domain

The domain of a function is the set of all possible values of x

The domain of the quadratic function is the interval

(-∞,∞)

All real numbers

step 2

Find the range

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have a vertical parabola open downward

The vertex is a maximum

Let

(h,k) the vertex of the parabola

so

The range is the interval

(-∞,k]

Find the vertex

f(x)=-x^2+14x-48

Factor -1 the leading coefficient

f(x)=-(x^2-14x)-48

Complete the square

f(x)=-(x^2-14x+49)-48+49

f(x)=-(x^2-14x+49)+1

Rewrite as perfect squares

f(x)=-(x-7)^2+1

The vertex is the point (7,1)

therefore

The range is the interval

(-∞,1]

6 0
3 years ago
Including 5% sales tax, an inn charges $252 per night. Find the inn’s nightly cost before the tax is added
stira [4]

Hi,

To find the cost before tax, we must find out how much the tax is. So we multiply 252 x .05 to get 12.6. So we know the tax was 12.6 dollars. Now all we have to do is subtract that from the total to get our answer. 252 - 12.6 = 239.4.

Have a great day!

3 0
3 years ago
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