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dolphi86 [110]
3 years ago
9

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe

n we began her study, the frog population was estimated at 1200, which function represents the frog population after x years?
Mathematics
1 answer:
Rama09 [41]3 years ago
5 0

You can see how this works by thinking through what's going on.

 

In the first year the population declines by 3%.  So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200.  3% of 1200 is the same as .03 * 1200.  So the population at the end of the first year is 1200 - .03 * 1200.  That can be written as 1200 * (1 - .03), or 1200 * 0.97

 

What about the second year?  The population starts at 1200 * 0.97.  It declines by 3% again.  But 3% of what???  The decline is based on the population at the beginning of the year, NOT based no the original population.  So the decline in the second year is 0.03 * (1200 * 0.97).  And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year.  So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.

 

So there's a pattern.  If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.

 

So the population after x years is 1200 * 0.97x

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3 years ago
1) The number √ , where n is a prime number is
Firlakuza [10]
It is an irrational number
3 0
3 years ago
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3. Laura walks 3/5 mile to school each day. Isaiah walk to school is 3 times as long as Laura's. Howfar does Isaiah walk to scho
Finger [1]
Lets write down what we know...

Laura walks 3/5 mile to school everyday

Laura=3/5mile

Isaiah's walk is 3 times as long as Lauras, so

Isaiah=Laura*3

We know how far Lauras walk is so we can solve for Isaiah's walk

Isaiah=3/5*3 (or Isaiah=3/5+3/5+3/5 if thats easier for you to solve for)
Isaiah=9/5 miles

Now we know the answer! Great, Isaiah walks 9/5 miles to school each day. But 9/5 is an improper fraction, so lets convert it to a mixed number.

9/5=

To solve for this, we have to find out how many times 5 can go into 9. 5 goes into 9 one time with a remainder of 4, so we can write the mixed number as.

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5 0
3 years ago
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Help thanksSSSSSSSSSS
Setler79 [48]

Answer:

  • \boxed{\sf{x=24}}

Step-by-step explanation:

<u>GIVEN:
</u>

To find the missing number in the proportion, you have to isolate it the term of x from one side of the equation.

\sf{\dfrac{8}{7}=\dfrac{x}{21}  }

First, thing you do is switch sides.

\sf{\dfrac{x}{21}=\dfrac{8}{7}  }

Multiply by 21 from both sides.

\Longrightarrow: \sf{\dfrac{21x}{21}=\dfrac{8*21}{7} }

Solve.

Multiply the numbers from left to right.

Use the order of operations.

PEMDAS stands for:

  • Parentheses
  • Exponents
  • Multiply
  • Divide
  • Add
  • Subtract

\Longrightarrow: \sf{\dfrac{8*21}{7}=\dfrac{168}{7}=24 }

\Longrightarrow: \boxed{\sf{x=24}}

  • <u>Therefore, the final answer is x=24.</u>

I hope this helps. Let me know if you have any questions.

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