Betsy started a business 2 years ago. She had 8 customers in the first year. She added 18 customers in the second year. Betsy's goal is that in each of the next 4 years, she will have three times ad many customers as the year before. Betsy shows her calculations in the TABLE below that if she meets this goal each year, she will have 312 customers 4 years from now. is Betsy correct? Use the drop-down menus to explain your reasoning.

Expression: (8 + 18) * 3^4
Step 1: 26 * 3^4 <<< TABLE
Step 2: 26 * 12
Answer: 312

Pick the correct answer in parentheses:
Betsy's calculations in Step 1 are ( is she Correct or Incorrect) because... ( .She added incorrectly .She has 26 customers at the end of her second year .She should have multiplied 18 * 3^4 before adding 8)

Besty's calculations in Step 2 are ( is she Correct or Incorrect) Because.... ( .She did not find the correct value of 3^4 .26 * 3^4 = 26 * 12 .She did not apply the order of operations correctly)

If Betsy reaches her goal each year, she will have.. ( .2,106 .312 .1,466) customers 4 years from now.

Betsy isn't correct. Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

Step-by-step explanation:

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

- Betsy started her business 2 years ago.

- In the first year, Betsy has 8 customers.

- In the second year, Betsy added 18 customers,

- So, her customers are now 8+18 = 26

- Betsy's goal is that in each of the next 4 years, she will have three times as many customers as the year before.

If the base number of customers is truly 26 this year,

Next year, Betsy would have 26 × 3 = 78 customers.

In 2 years, she would have 78 × 3 = 234

Thus indicating that in t years from now, the number of her customers will be

N(t) = N₀ × 3ᵗ

where

N(t) = number of customers t time from now

N₀ = number of customers at the moment = 26

t = number of years from now.

N(t) = 26 × 3ᵗ

In 4 years from now, Betsy will have

N(t=4) = 26 × 3⁴ = 2,106

So, it is evident that Betsy's calculations are wrong as she made her calculations by multiplying the base number of customers by 3 and then summing it all up for the 4 years under review instead of a continuous multiplication by 3.

26 × 3 × 4 is different from 26 × 3⁴

- If Betsy meets her target for the next 4 years, she will have 2106 customers in 4 years time.

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