Based on this projection, which of the following is closest to the number of t-shirts Marcus needs to sell during the first month to meet his goal? (100 brainley points plsss help)

The number of T-shirts Marcus needs to sell each month to meet his goal of 15,000 T-shirts in 6 months is 15,000 / 6 = <<15000/6=2500>>2,500 T-shirts per month.

His projection is that the number of T-shirts he sells will increase by 20% each month, which means that he needs to sell 20/100 * 2,500 = 500 more T-shirts each month than the previous month.

To meet his goal of selling 2,500 T-shirts during the first month, Marcus needs to sell a total of 2,500 - 500 = <<2500-500=2000>>2,000 T-shirts during the first month.

Therefore, the closest answer to the number of T-shirts Marcus needs to sell during the first month to meet his goal is B) 2,000.

Hope this helps you

semsee45 semsee45 · Answer 2 · 2022-12-18T13:44:45+01:00

Answer:

A. 1,500

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]

The given scenario can be modelled as a geometric series.

If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:

Sum Sₙ = 15,000
n = 6

If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:

r = (1 + 0.2) = 1.2

Substitute these values into the formula and solve for a:

[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]

[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]

[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]

[tex]\implies a=1510.586188[/tex]

Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.

Check:

Month 1 = 1511
Month 2 = 1511 × 1.2 = 1813
Month 3 = 1813 × 1.2 = 2176
Month 4 = 2176 × 1.2 = 2611
Month 5 = 2611 × 1.2 = 3133
Month 6 = 3133 × 1.2 = 3760

Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004

Check:

Month 1 = 1500
Month 2 = 1500 × 1.2 = 1800
Month 3 = 1800 × 1.2 = 2160
Month 4 = 2160 × 1.2 = 2592
Month 5 = 2592 × 1.2 = 3110
Month 6 = 3110 × 1.2 = 3732

Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000