Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The fish population of Lake Collins is decreasing at a rate of 4% per year. In 2004 there were about 1,150 fish. Write an exponential decay function to model this situation. Then find the population in 2009.

A: y = 1,150(0.96)^t
2009=938
B: y = 1,150(0.96)^t
2009=942.67
C: y = 1,150(0.6)^5
2009=89
D: y = 1,150(0.04)^t

Sagot :

mhanifa

Answer:

  • Option A

Step-by-step explanation:

Decrease rate is 4%

  • 1 - 4% =
  • 1 - 0.04 =
  • 0.96

The equation for this situation is

  • [tex]y = 1150*0.96^t[/tex], where t is the number of years passed since 2004

The fish population in 2009

  • [tex]y = 1150*0.96^{2009-2004}=1150*0.96^5 = 938 (rounded)[/tex]

Correct choice is A

semsee45

Answer:

[tex]\textsf{A:} \quad y = 1150(0.96)^t[/tex]

      2009 = 938

Step-by-step explanation:

Exponential Function

General form of an exponential function:

  [tex]y=ab^x[/tex]

where:

  • a is the initial value (y-intercept)
  • b is the base (growth/decay factor) in decimal form
  • x is the independent variable
  • y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the rate of decrease is 4% per year, that means that each year the number of fish is 96% of the previous year, since 100% - 4% = 96%

Given:

  • a = 1150
  • b = 96% = 0.96
  • x = t = time in years
  • y = total of fish

Substitute the given values into the exponential equation:

[tex]\implies y=1150(0.96)^t[/tex]

If the initial year was 2004 then:

⇒ t = 2009 - 2004 = 5

Substitute t = 5 into the equation and solve for y:

[tex]\implies y=1150(0.96)^5[/tex]

[tex]\implies y=937.6786022...[/tex]

Therefore, the population in 2009 was 938 (to the nearest whole number).

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.