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Marrrta [24]
3 years ago
5

How can i calculate the growth rate of the values below

Mathematics
1 answer:
Grace [21]3 years ago
8 0

Answer:

  12%

Step-by-step explanation:

The equation for the growth is ...

  f(t) = (initial value)×(growth multiplier per period)^(number of periods)

where the growth multiplier is often expressed as a percentage added to 1:

  multiplier = 1+r

  growth rate = r

__

This equation has two unknowns:

  • initial value
  • growth multiplier

In order to find these, you can make use of two of the supplied data points. I like to choose the ones that are farthest apart, as they tend to average out any errors due to rounding.

Clearly, the table tells you the initial value is 210. If you don't believe, you can put the numbers in the equation to see that:

  f(0) = (initial value)×(growth multiplier)^0

  210 = (initial value)×1

  (initial value) = 210

__

Using the last data point, we get ...

  f(7) = 210×(growth multiplier)^7

  464 = 210×(growth multiplier)^7 . . . . . . . . . fill in table value

  2.209524 = (growth multiplier)^7 . . . . . . .  divide by 210

You can solve this a couple of ways. My calculator is able to take the 7th root, so I can use it to find ...

  \sqrt[7]{2.209524}=\text{(growth multiplier)}\\1.119916\approx \text{(growth multiplier)}

Alternatively, you can use the 1/7 power:

  2.209524^(1/7) = (growth multiplier)

Another way to solve this is to use logarithms:

  log(2.209524) = 7×log(growth multiplier) . . . . . take the log

  log(2.209524)/7 = log(growth multiplier) . . . . . divide by 7

  0.04918553 ≈ log(growth multiplier)

  growth multiplier = 10^0.04918553 ≈ 1.11992 . . . . take the antilog

So, our growth multiplier is ...

  1 + r ≈ 1.11992

  r ≈ .11992 ≈ 12.0%

The rate of growth is about 12% in each period.

_____

Collapsing all of that to a single calculation:

  growth rate = (464/210)^(1/(7-0)) -1 ≈ 12.0%

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The slope is 7/5 and the equation of the line is 5y - 7x = 0 if the points ​(10​,14​) and ​(35​,49​) form a proportional relationship.

<h3>What is the slope?</h3>

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

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Learn more about the slope here:

brainly.com/question/3605446


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