"Help Please Thanks"Judah makes pottery to sell at his school’s craft bazaar. Every year, he determined that he makes Twenty- five Dollars less than he made the previous year. Write a function rule to define the total amount y Judah made based on the amount x he made the previous year. Give an example of how the function rule works. Which is the dependent variable? The independent variable?

Question

"Help Please Thanks"Judah makes pottery to sell at his school’s craft bazaar. Every year, he determined that he makes Twenty- five Dollars  less than he made the previous year. Write a function rule to define the total amount y Judah made based on the amount x he made the previous year. Give an example of how the function rule works. Which is the dependent variable? The independent variable?

parthkohli · Answer

$\Large \color{MidnightBlue}{\Rightarrow m_{x} = m_{x + 1} - 25 }$

parthkohli · Answer

$\Large \color{MidnightBlue}{\Rightarrow x - 25 = y }$

parthkohli · Answer

So, the dependant variable would be the one which changes the value depending on another variable.

apoorvk · Answer

Let 'a' be the amount Judah made in his very first year.
so, every year, he earns 25 bucks lesser
that means, the very next year, he earned x-25
and the year after that, x-25-25
and so on....

so you do realise that we have an AP in here, right?

the first term is 'a'
the common difference is '-25'
and the year till which we have to calculate the total earnings is 'n', suppose

so earning till the nth year will be sum of the AP till 'n' terms

Sum 'S' of an AP with initial term 'a', common difference 'd', and no. of terms 'n' is:
$$S=\frac n 2 (2a + (n-1)d)$$

substitute 'a', and 'd'. and you get your required expression.

parthkohli · Answer

^ OMG

anonymous · Answer

@ParthKohli  and @apoorvk  thanks for helping her :) you guyz are awesome