Ineed . basically, i need to figure out the dependent and independent value of a function.

here is the situation thing:
the chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. the number of students is modeled by f(x) = 4(1.0256)x.
i had to make like a question about it. i chose "in how many weeks would there be 12 students? ".
so that made the equation 12 = 4(1.0256)x.
then i had to use logarithms to get to the answer (i got 43.46, if you could fact check this too, that would be lovely.)

so the question is:
let your dependent variable in the function be y. write the function that models the independent variable in terms of y, using logarithms.

i really don't know what it wants me to do,

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

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !