1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Usimov [2.4K]
3 years ago
11

Devise the exponential growth function that fits the given data, then answer to accompanying question. Be sure to identify the r

eferences point (t = 0) and The current population of a town is 70,000 and is growing exponentially. If the population to be 75,000 in 10 years, then what will be the populations 20 years What is the reference point (t = 0)? the initial population 70,000 the current year the population in 10 years, 75,000 What are the units of time? percent people decades years Write the exponential growth function. Round any numerical values to three decimal places as needed. y(t) = What is the population 20 years from now?
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
7 0

Answer:

In 20 years, the population will be about 80.3 thousand people

Step-by-step explanation:

If our first time is 0 and the population that goes along with that time is 70,000, we have a coordinate point where x is the time (0), and y is the population at that time (70).  Our next time is 10 years later, when the population is 75,000.  The coordinate point for that set of data is (10, 75).  Now we will use those 2 points in the standard form of an exponential equation to write the model for this particular situation.  

Exponential equations are of the form

y=a(b)^x

where x and y are the coordinates from our points, one at a time; a is the initial value, and b is the growth rate.  Filling in an equation with the first set of data:

70=a(b)^0

Anything raised to the power of 0 = 1, so b to the power of 0 = 1 and we simply have that a = 70.

Now we use that value of a along with the x and y from the next coordinate pair to solve for b:

75=70(b)^{10}

Begin by dividing both sides by 70 to get

1.071428571=b^{10}

Undo the power of 10 on the right by taking the 10th root of both sides:

(1.071428571)^{\frac{1}{10}}=(b^{10})^{\frac{1}{10}}

On the right side we simply have b now, and on the left we have

1.006923142=b

Now we have a and b to write the model for this situation:

y=70(1.006923142)^x

We need to find y, the population, in x = 20 years:

y=70(1.006923142)^{20}

Raise the parenthesis to the 20th power giving you

y = 70(1.147959784) and

y = 80.3 thousand people

You might be interested in
Which formula do you need to convert 77º F into kelvins?
MA_775_DIABLO [31]

K = (y °F – 32) ÷ 1.8 + 273.15 or K = (y °F – 32) x 5/9 + 273.15

8 0
3 years ago
Read 2 more answers
What is the apr for a $585 tablet with 12 payments of $50.81
JulsSmile [24]

Answer:

the answer is 4%

Step-by-step explanation:

585/12=48.75

50.81-48.74=2.06

now 2.06 that's the money from interest rate

so now 2.06/50.81=0.04

so the answer is 4%

3 0
3 years ago
The university took a phone survey of 3421 students about tuition. Of the students surveyed 2004 of those students believed that
Nat2105 [25]
Is the answer c or d i say c
8 0
2 years ago
Read 2 more answers
Income Statements under Absorption Costing and Variable Costing
kotykmax [81]

The estimated income statement for the month shows a loss of $840000.

<h3>How to illustrate the income statement?</h3>

The estimated income statement for the month will be:

Sales = $25,600,000

Less: Cost of goods sold

Direct materials (320000 × 15) = $4,800,000

Direct labor (320000 × 17) = $5,440,000

Variable costing (320000 × 15) = $11,200,000

Fixed manufacturing cost = $1,530,000

Total cost of goods sold = $22970000

Gross profit = $25,600,000 - $22970000 = $2,630,000

Gross profit = $2,630,000

Less:

Variable selling and administrative expense = $3200000

Fixed selling and administrative = $270000

Loss from operations = $840000

Therefore, the estimated income statement for the month shows a loss of $840000.

Learn more about income statement on:

brainly.com/question/15169974

#SPJ1

5 0
1 year ago
How many pounds of a 15% copper alloy must be mixed with 700lb of a 30% copper alloy to maybe a 25.5% copper alloy
lisov135 [29]

Answer:

300\; \rm lb.

Step-by-step explanation:

Let x represent the mass (in pounds) of that 15\% copper alloy required, such that the final mixture would contain 25.5\% copper by mass.

Consider: if x pounds of that 15\% copper alloy is mixed with 700 pounds that 30\% copper alloy, what would be the mass of copper in the mixture?

  • Mass of copper in x pounds of that 15\% copper alloy: (0.15\, x)\; \rm lb.
  • Mass of copper in 700 pounds of that 30\% copper alloy: 700 \times 0.30 = 210\; \rm lb.

Therefore, the mixture would contain (210 + 0.15\, x) \; \rm lb of copper.

The mass of that mixture would be (700 + x)\; \rm lb. The mass fraction of copper in that mixture would be:

\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\%.

This ratio is supposed to be equal to 25.5\%. These two pieces of equations combine to give an equation about x:

\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\% = 25.5\%.

\displaystyle \frac{210 + 0.15\, x}{700 + x} = 0.255.

Simplify and solve for x:

210 + 0.15\, x= 0.255\, (700 + x).

(0.255 - 0.15)\, x= 210 - 0.255 \times 700.

\displaystyle x = \frac{210 - 0.255 \times 700}{0.255 - 0.15} = 300.

Therefore, 300\; \rm lb of that 15\% alloy would be required.

4 0
3 years ago
Other questions:
  • You start an account with $500 and an interest rate of 6% compounded yearly. How much is in the account after 3 years?
    9·1 answer
  • What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 degrees
    15·1 answer
  • The perimeter of a regular decagon is 624m. State the length of one of its sides
    14·1 answer
  • Enter the fraction as a decimal and a percent
    12·1 answer
  • Omg help me thissssss plsssss
    12·1 answer
  • 1. 20% of what number is 18?
    11·1 answer
  • Add the mixed number fractions. Simplify, if possible.
    9·1 answer
  • If one-third of one-fourth of a number is 15, then three-tenth of that number is:
    12·1 answer
  • Help I have 30 in Math
    9·2 answers
  • Solve each triangle: Find all the missing sides and angles. Round answers to the nearest tenth.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!