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evablogger [386]
3 years ago
15

I need help. Basically, I need to figure out the dependent and independent value of a function.

Mathematics
1 answer:
Rama09 [41]3 years ago
6 0

Answer:

  • x = log(y/4)/log(1.0256)
  • your answer for y=12 is correct

Step-by-step explanation:

The question is asking you to solve ...

   y = f(x)

for x. (In other words, find the inverse function.)

You already did this using a constant for y. Do the same thing with y instead of the constant.

  y = 4(1.0256^x)

  y/4 = 1.0256^x . . . . . . . divide by 4

  log(y/4) = x·log(1.0256) . . . . . take logs

  log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x

Now, you have a model for x in terms of y, which is what the question is asking for.

  x = log(y/4)/log(1.0256) . . . . . . . exact expression

When y=12, this is ...

  x = log(12/4)/log(1.0256) ≈ 43.46 . . . . weeks

_____

This is a linear equation in log(y), so can be written as such:

  x = 91.0912·log(y) -54.8424 . . . . . approximate expression

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Charra [1.4K]

Percentage of yellow leaves on a tree during Autumn = 40%

Percentage of green leaves on a tree during Autumn = 24%

Percentage of half yellow leaves on the tree during Autumn :

=  \tt100 - 40 + 24

= \tt 100 - 64

= \tt 36 \%Thus, the percentage of half yellow leaves on the tree during Autumn = 36%

Number of half yellow leaves on the tree = 36%

Let the total number of leaves on the tree be x.

Which means :

=  \tt36 \% \: of \: x = 72

=  \tt \frac{36}{100}  \times x = 72

=  \tt \frac{36 \times x}{100}  = 72

=  \tt \frac{36x}{100}  = 72

= \tt 36x = 72 \times 100

=  \tt36x = 7200

= \tt x =  \frac{7200}{36}

\color{plum} =  \tt \: x = 200

Thus, total number of leaves on the tree = 200

Number of yellow leaves on the tree :

=  \tt40 \% \: \:  of \: \:  200

=  \tt \frac{40}{100}  \times 200

= \tt   \frac{40 \times 200}{100}

= \tt  \frac{8000}{100}

\color{plum}  \tt = 80 \: yellow \:  \: leaves

Thus, total number of yellow leaves on the tree = 80

Number of green trees on the tree :

=  \tt24 \% \:  \: of \:  \: 200

= \tt  \frac{24}{100} \times 200

= \tt  \frac{24 \times 200}{100}

=  \tt \frac{4800}{100}

\color{plum} = \tt 48 \: green \:  \: leaves

Thus, the total number of green leaves on the tree = 48

Since the sum of all types of leaves form 200[80+48+72=200], we can conclude that we have found out the correct number of each type of leaf.

▪︎Therefore, <em>the total number of leaves on the tree = 200</em>

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There are 532 more birds than snakes.

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