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aivan3 [116]
3 years ago
7

Write a linear equation that has a slope of 1/2 and a y-intercept at the origin.

Mathematics
1 answer:
Nata [24]3 years ago
5 0

Answer:

y=1/2x

Step-by-step explanation:

Slope intercept form is the most commonly used linear equation:

It goes like this:

y=mx+b

In this equation, m is the slope and b is the y-intercept.

Your line has a slope of 1/2. So, your m-value is 1/2.

y=1/2x+b

B, your y-intercept, is at the origin.

The origin is the point (0,0).

So b, is 0 (y-intercept is the y-value when x is 0)

y=1/2x+0

=

y=1/2x

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  2. 6400
  3. 5.0

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The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.

1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.

  population = (initial population) × (growth factor)^(t/(growth period))

where the "growth period" is the period of time in which the population is multiplied by the "growth factor".

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__

2) Putting t=8 into the formula, we get ...

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After 8 hours, the population will be 6400.

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3) Fill in the given number and solve for t.

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  2270/400 = 2^(t/2)

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  log(227/40) = (t/2)log(2)

  t = 2×log(227/40)/log(2) ≈ 5.009

After 5.0 hours, the population will reach 2270.

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