Find the sum of a finite geometric series. the smiths spent $2,000 on clothes in a particular year. if they increase the amount they spend on clothes by 10% each year, the smiths will spend a total of $ on clothing in 4 years.

Including the first year where they spend $2,000 dollars and it's added altogether: $9,282

Not including first year and it's added altogether: $10,210.2

If you're talking about the money they spent on only the 4th year:
1st year- $2,000
2nd year- $2,200
3rd year- $2,420
4th year- $2,662

If you don't count the year where they spend $2,000:
1st year: $2,200
2nd year: $2,420
3rd year: $2,662
4th year: $2,928.2

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204