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
ziro4ka [17]
3 years ago
12

Toxic Pollution: In the first year of a study, health officials discovered toxic pollutants in the soil surrounding a factory. T

he initial measurement was 65 parts per million (ppm) of pollutant. They returned to take similar measurements for several years afterward, and uncovered a disturbing trend. The pollutant levels in the soil surrounding the factory were growing exponentially, at a rate of 4.5% each year. Which exponential model predicts the amount of pollutant in the soil t years from the first measurement?
Mathematics
1 answer:
ella [17]3 years ago
3 0

Answer:

The model for the pollutant levels in the soil t years from the first measurement is:

Y(t)=65e^{0.044}

Step-by-step explanation:

We have a first measurement of 65 parts per million (ppm) of pollutant.

We also know that the pollutant levels were growing exponentially at a rate of 4.5% a year.

We can model this as:

Y(t)=Y_0e^{kt}

The value of Y0 is the first measurement, that correspond to t=0.

Y_0=65

The ratio for the pollutant levels for two consecutive years is 1+0.045=1.045. This can be expressed as the division between Y(t+1) and Y(t), and gives us this equation:

\dfrac{Y(t+1)}{Y(t)}=\dfrac{Y_0e^{k(t+1)}}{Y_0e^{kt}} =\dfrac{e^{k(t+1)}}{e^{kt}}=e^{k(t+1-t)}=e^k=1.045\\\\\\k=ln(1.045)\approx 0.044

Then, we have the model for the pollutant levels in the soil t years from the first measurement:

Y(t)=65e^{0.044}

You might be interested in
What is the slope of a line that is perpendicular to the line y = -1/4 -1<br>​
DerKrebs [107]
Y = 4x - 1

The slope here is “4”
8 0
2 years ago
Determine the negation of the following statement:<br><br> x is not equal to 50.
Lana71 [14]
Any more details? I cannot know if you don’t have any more details for me
4 0
2 years ago
209.106 in word form
Scrat [10]
In mathematics, number with a symbol of a point, is expressed in decimal form. When they are read, the numbers after the decimal point are read digit after digit. Therefore, in word form, the number is read as: Two hundred nine point one zero six.
8 0
3 years ago
Read 2 more answers
Interval is 0, 2pi) 4 sin^2x-4 sin x + 1 = 0
svetoff [14.1K]

Answer:

\large\boxed{x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}}

Step-by-step explanation:

4\sin^2x-4\sin x+1=0\\\\2^2\sin^2x-2(2\sin x)(1)+1^2=0\\\\(2\sin x)^2-2(2\sin x)(1)+1^2=0\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(2\sin x-1)^2=0\iff2\ain x-1=0\qquad\text{add 1 to both sides}\\\\2\sin x=1\qquad\text{divide both sides by 2}\\\\\sin x=\dfrac{1}{2}\to x=\dfrac{\pi}{6}\ \vee\ x=\dfrac{5\pi}{6}

8 0
3 years ago
6. A garbage truck collects trash from
8_murik_8 [283]
The answer should be 97 trash cans…
6 0
1 year ago
Other questions:
  • 445.3 round to the nearest ten thousand
    13·1 answer
  • Explain how you would draw a box-and-whisker plot for the data below.
    13·1 answer
  • Can you help me lol and actually show your work and how you got your answer please and thank you!
    7·2 answers
  • If x = 2/9 and y = 3/7 work out the value of x + y
    6·2 answers
  • Classify each of the following number
    5·1 answer
  • Which point on the number line shown would represent the fraction 3/20?
    15·1 answer
  • Toby read a total of 12 books over 3 months. If Toby has read 16 books so far, how many
    11·2 answers
  • PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
    9·2 answers
  • What is the area of a triangle with vertices at (−2, 1), (2, 1), and ​(3, 4)​ ?
    13·1 answer
  • A = 1 , b =3.5 i need help quick
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!