2022-04-29

The exponential models describe the population of the indicated country, A, in millions, t years after

2006.

Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?

karton

Expert2022-07-07Added 613 answers

the general formula for continuous compounding is:

A = p * e^(rt)

A is the future value

p is the present value

r is the continuous compounding growth rate per time period.

t is the numbe of time periods.

the time periods for this problem are expressed in years.

the country with the highest value of r has the highest continuous compounding growth rate.

that country would be iraq with a continuous compounding growth rate of .027 per year.

to convert from continuous compounding growth rate to annual compounding growth rate, use the following formula.

(1+ar) = e^cr

when cr = .027, that formula becomes:

(1+ar) = e^.027 = 1.027367803

to solve for ar, subtract 1 from both sides of the equation to get:

ar = .027367803.

that's the annual compounding growth rate.

the annual compounding growth rate percent is equal to 2.7367803%.

the population in iraq is growing at a rate of 2.7367803% per year.

since the formulas are equivalent, they should yield the same result.

using continuous compounding formula for 1 year:

26.8 * e^.027 = 27.53345711

using annual compounding formula for 1 year:

26.8 * (1.027367803) = 27.53345711

they're the same, confirming that the two formulas are equivalent.

the annual growth rate for all of the countries is shown below:

india:

e^.014 = 1.014098459 - 1 = .014098459 = 1.4098459%

iraq:

e^.027 = 1.027367803 - 1 = .027367803 = 2.7367805%

japan:

e^.001 = 1.0010005 - 1 = .0010005 = 1.0005%

russia:

e^-.004 = .9960079893 - 1 = -.0039920107 = -.39920107%

The polynomial P(x) of degree 4 has

a root of multiplicity 2 at x=4

a root of multiplicity 1 at x=0 and at x=-2

It goes through the point (3,-75)

Find a formula for P(x)find a polynomial f(x) of degree 4 with real coefficients and the following zeros -3(multiplicity of 2), -i

make a polynomial from zeros 5+3i, 5-3i, -1

Name the first five of the arithmetic sequence.

a1=-12, d=-10

first term:

second term:

third term:

fourth term:

fifth term:

for the polynomial below, -2 is zero

h(x)=x^3-6x-4

Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:

Number of years 1 2 3 Car 1 (value in dollars) 17,390 16,346.60 15,365.80 Car 2 (value in dollars) 17,500 16,500 15,500 **Part A:**What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)**Part B:**Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)**Part C:**Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)Source StylesNormalFontSize

Express x^2+8x+15 in the form (x+a)^2+b

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Part 1

Luis and Raul are riding their bicycles to the beach from their respective homes. Luis proposes that they leave their respective homes at the same time and plan to arrive at the beach at the same time. The diagram shows Luis's position at two points during his ride to the beach. Write an equation in slope-intercept form to represent Luis's ride from his house to the beach. If Raul lives 5 miles closer to the beach than Luis, at what speed must Raul ride for the plan to work? x -4 -2 0 6 y -11 10 13 5+7x=4y

-4x≤-16 or 2x-18≥-4

$if\frac{4{x}^{2}y}{3z}\times \frac{a}{b}=\frac{4x}{{z}^{2}},writeexpressionsforaandb.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}a=?\phantom{\rule{0ex}{0ex}}b=?$

f(c) =-5-2l-2x+1l

what is the aspect of each part for this algebraic expression $4{x}^{2}-2=5+7x$?