Response:
Betsy's calculations are inaccurate. Instead of continuously multiplying the base number of customers by 3, she incorrectly summed the base number multiplied by 3 across 4 years.
26 × 3 × 4 is not the same as 26 × 3⁴
- If Betsy achieves her goal over the next 4 years, she will have 2,106 customers at that time.
Detailed Breakdown:
- Betsy launched her business 2 years ago.
- She had 8 customers in her first year.
- In the subsequent year, she gained an additional 18 customers,
- Bringing her total to 8 + 18 = 26 customers.
- Betsy's aim is to triple her customer count each year over the next 4 years.
If 26 is her current customer base,
next year, she would then have 26 × 3 = 78 customers.
In the following 2 years, that number would reach 78 × 3 = 234
Thus, the projection for her customers in t years is:
N(t) = N₀ × 3ᵗ
where
N(t) = number of customers in t years
N₀ = current customer count = 26
t = years in the future.
N(t) = 26 × 3ᵗ
In 4 years, Betsy will have
N(t=4) = 26 × 3⁴ = 2,106
Therefore, it's clear that Betsy's calculations are incorrect because she summed the base customers multiplied by 3 for all 4 years instead of applying a continuous multiplication by 3.
26 × 3 × 4 does not equal 26 × 3⁴
- If Betsy successfully meets her targets over the following 4 years, she is projected to have 2,106 customers in 4 years.
Hope this is helpful!!!
