Question 143·200 Super-Hard SAT Math Questions·Advanced Math
A video channel had 12,000 subscribers 3 days ago. The number of subscribers grows exponentially and triples every 40 hours.
Which choice gives a function that models the number of subscribers weeks from now, written in the form , where and are constants? Anікo Questiοn Bank
Translate the situation into an exponential model by (1) converting all time units to match the given growth period, (2) dividing by the period length to get the exponent, and (3) using exponent rules to rewrite the result in the requested base. For base changes like 3 to 9, use so . Writtеn by Аnikо
Hints
Convert to hours first
Convert 3 days and weeks into hours, then add them to get total hours since 3 days ago.
Turn time into an exponent
Because the count triples every 40 hours, the exponent on 3 is the number of 40-hour intervals: (total hours)/40.
Switch from base 3 to base 9
Use . A helpful identity is . А-n-і-к-ο.ai
Desmos Guide
Enter each choice as a function
In Desmos, enter each option as a separate function, for example:
S1(x)=12000*3^(9/5)*9^((21/10)x)S2(x)=12000*3^(9/5)*9^((21/5)x)- etc.
Check the value at
At (today), the model should give
Use the table to compare each function’s value at to this target.
Check the weekly growth factor
From to (one week later), the exponent on 3 should increase by , so the multiplier should be . The correct function will be consistent with both the value and this weekly multiplier.
Step-by-step Explanation
Convert the time from 3 days ago to weeks from now into hours
3 days is hours.
weeks is hours.
Total elapsed time from 3 days ago to weeks from now is hours.
Convert hours to 40-hour tripling intervals
Each 40-hour interval multiplies the subscribers by 3, so the number of tripling intervals is
So
Rewrite the -dependent part using base 9
Separate the constant and -dependent parts:
Since , we have . Thus,
Write and match a choice
Substitute the base-9 rewrite: (Аniкo.аi)
So the correct choice is .