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mervesena01
28.01.2020 •
Mathematics
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,
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Ответ:
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
Ответ:
what do you mean
have a great day