Answer:
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.
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.
Step-by-step explanation:
- 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.
Hope this Helps!!!
But, this can be factored further. 