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ANTONII [103]
2 years ago
5

Find the exponential function that passes through the points (2,80) and (5,5120)​

Mathematics
1 answer:
juin [17]2 years ago
3 0

Answer:

  y = 5·4^x

Step-by-step explanation:

If you have two points, (x1, y1) and (x2, y2), whose relationship can be described by the exponential function ...

  y = a·b^x

you can find the values of 'a' and 'b' as follows.

Substitute the given points:

  y1 = a·b^(x1)

  y2 = a·b^(x1)

Divide the second equation by the first:

  y2/y1 = ((ab^(x2))/(ab^(x1)) = b^(x2 -x1)

Take the inverse power (root):

  (y2/y1)^(1/(x2 -x1) = b

Use this value of 'b' to find 'a'. Here, we have solved the first equation for 'a'.

  a = y1/(b^(x1))

In summary:

  • b = (y2/y1)^(1/(x2 -x1))
  • a = y1·b^(-x1)

__

For the problem at hand, (x1, y1) = (2, 80) and (x2, y2) = (5, 5120).

  b = (5120/80)^(1/(5-2)) = ∛64 = 4

  a = 80·4^(-2) = 80/16 = 5

The exponential function is ...

  y = 5·4^x

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artcher [175]

The length of the bridge is 12.12 feet.

The length the dog swam is 32.36 feet.

The situation forms a right angle triangle.

<h3>What is a right angle triangle?</h3>

A right angle triangle has one of its angles as 90 degrees. Therefore, the sides and angle can be found using trigonometric ratios.

The length of the bridge is the opposite side of the triangle and the length the dog swim is the hypotenuse side of the triangle.

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Let's find the length of the bridge as follows:

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7 0
2 years ago
(40 POINTS)
34kurt

Answer:

1.   y= 25400(1 + 0.11)^x

2.  2019

Step-by-step explanation:

1. y = a(1 + r)^x       <em> </em>

<em>(exponential growth formula :</em>

<em>a = initial value (the amount before measuring growth or decay) </em>

<em>r = growth or decay rate (usually represented as a percentage and expressed as a decimal) </em>

<em> x = number of time units that have passed)</em>

y= 25400(1 + 0.11)^x

so in 1 year, in 1996, we would say

y=25400(1+0.11)^1

y=25400(1.11)

y=28194

2. I found the answer by plugging in numbers into x

with x = 24

y= 25400(1+0.11)^24

y= 310874

so in 24 years, the population will surpass 302438 which would be 1995+24= 2019

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