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
Lilit [14]
3 years ago
9

Assume the exponential growth model ​A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

2006. If the population must stay below 2424 billion during the next 100​ years, what is the maximum acceptable annual rate of​ growth?
Mathematics
1 answer:
Whitepunk [10]3 years ago
8 0

Answer:

1.4% is the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model ​is given by:

A(t) = A_0e^{kt}

where k is the growth rate, t is time in years and A_0 is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

A_0 = 5.9\text{ billions}

We have to find the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.

Putting these values in the growth model, we have,

24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%

1.4% is the maximum acceptable annual rate of​ growth such that the population must stay below 24 billion during the next 100​ years.

You might be interested in
Sarah started with 50 dollars in her bank account. Each month, she puts 25 more dollars in her account. The amount of money in d
Basile [38]


D=25m+50

D=(25)(8)+50

D=200+50

D=250

There will be $250 after 8 months.

5 0
3 years ago
Read 2 more answers
Perform each of the following computations using the measured quantities below.
mylen [45]
<h2>Question </h2>

Perform each of the following computations using the measured quantities below.

Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).

a. 917.2 + 45.63 = ___________

b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

<h2>Answer:</h2>

(a) 9.6 x 10²

(b) -6.1 x 10⁻³

<h2>Step-by-step explanation:</h2>

(a) 917.2 + 45.63

<em>First add the two numbers as follows (ensure that the decimal numbers are well aligned);</em>

   9  1   7 . 2

+   <u>   4  5 . 6  3</u>

   <u>9  6 2  . 8  3</u>

<u></u>

<em>To write the result in a proper scientific notation (one non-zero number to the left of the decimal point), </em>

i. Express the number is standard form

962.83 = 9.6283 x 10²

<em>Note that;</em>

From the result in (i)

9.6283 = mantissa

10 = base

² = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

9.6 x 10²

Therefore, the result in the proper scientific notation is <em>9.6 x 10²</em>.

(b)  3.423 x 10⁻⁴ - 6.42 x 10⁻³

Find the difference between the two numbers as follows;

i. Re-write the numbers so that they both have the same exponents:

0.3423 x 10⁻³ - 6.42 x 10⁻³

ii. Factor out 10⁻³

10⁻³(0.3423 - 6.42)

iii. Solve the bracket

10⁻³(-6.0777)

iv. Rewrite the result in (iii)

-6.0777 x 10⁻³

<em>To write the result in a proper scientific notation (one non-zero number to the left of the decimal point), </em>

i. Express the number is standard form

-6.0777 x 10⁻³       [already in standard form]

<em>Note that;</em>

From the result in (i)

-6.0777 = mantissa

10 = base

⁻³ = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

-6.1 x 10⁻³

Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.

6 0
3 years ago
The ideal width of a certain conveyor belt for a manufacturing plant is 50 in. an actual conveyor belt can vary from the ideal b
Nastasia [14]
50 + 7/32 = 50 7/32
50 - 7/32 = 49 25/32

answers are :
c.) 49 25/32 < = x < = 50 7/32
e.) |x - 50| < = 7/32
     

8 0
3 years ago
Peter borrowed a sum of R12 850.00 at the beginning of a year with a certain simple interest rate. After 14 quarters, in a diffe
ladessa [460]

The original annual simple interest rate, rounded to two decimal places, is 3.79%

What is the formula for simple interest?

The simple interest on a loan or deposit is determined as the principal multiplied by the simple interest rate and time

I=PRT

The first loan:

P=12 850.00

R=r(assume it is r)

T=4 years

I=12 850.00*r*4

I=51400r

The second loan was taken after 14 quarters the first was taken out, which is the same as after 3.5 years, hence, the interest on the second loan is only for a half a year

P=3 273.00

R=0.5r( half of the interest on the first loan)

T=0.5 years

I=3 273.00*0.5r*0.5

I= 818.25r

Total interest=51400r+818.25r

Total interest=52218.25r

total interest paid=1 980.00

1 980.00=52218.25r

r=1 980.00/52218.25

r=3.79%

Find out more about simple interest on: brainly.com/question/1115815

#SPJ1

5 0
2 years ago
At the ice cream parlor,sundaes cost $4.25 and waffle cones cost $3.75.You and your friends have $50 to spend.Your group buys 5
stich3 [128]

Answer:

You can buy 7 waffle cones.

Step-by-step explanation:

Let sundae = x

Let waffle cones = y

4.25x + 3.75y ≤ 50

4.25 (5) + 3.75y ≤ 50

21.25 + 3.75y ≤ 50

3.75y ≤ 28.75

y ≤ 7.666666666

* round to the nearest whole to get 7

6 0
3 years ago
Other questions:
  • at noon Aretha can watch a football game a basketball game or a documentary about horses on tv .at 3:00she can watch a different
    7·1 answer
  • What is h(x) =-3x2 - 6x + 5 written in vertex form?
    11·2 answers
  • Effective Rate find the effective rate of interest corresponding to a nominal rate of 7.5% per year compounded.
    14·1 answer
  • Use the side spittler theorem to find x given that PQ |BC
    15·2 answers
  • From the information in the diagram, what is H
    11·1 answer
  • The angle of elevation from a viewer to the top of a flagpole is 50°. The viewer is 80 ft away and the viewer's eyes are 5.5 ft
    14·1 answer
  • Standard form of 0=2-y
    11·2 answers
  • Which statement is true? 7.11≤−7.1 7.11&gt;−7.1 7.11&lt;−7.1 7.11=−7.1
    8·1 answer
  • Katrina is solving the equation -2(x+3)= 4(2x+3)-(x+4). Which equivalent equations might Katrina use? Check all that apply. Ox-2
    9·2 answers
  • WRITE and absolute value inequality for graph below, use X for your variable... PLEASE HELP IF CORRECT I WILL NEED HELP WITH TWO
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!