Betsy should not be correct. Betsy's calculations are incorrect because she made her calculations by multiplying the base number of customers by 3 and then add it all up for the 4 years under review rather of a continuous multiplication by 3.
[tex]26 \times 3 \times 4[/tex]is different from [tex]26\times 3^4[/tex]
In the case when 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 is
= 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.
In the case when the base number of customers is truly 26 this year,
Next year, Betsy would have 26 (3) = 78 customers.
So,
In 2 years, she would have 78 (3) = 234
Therefore, indicating that in t years from now, the number of her customers will be
[tex]N(t) = N_0 \times 3^t[/tex]
here
N(t) = number of customers t time from now
N₀ = number of customers at the moment = 26
t = number of years from now.
[tex]N(t) = 26 \times 3^t[/tex]
In 4 years from now, Betsy will have
N(t=4) = [tex]26 \times 3^4[/tex]
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