The number of customers that visit a local small business is 29,600 and has been continuously declining at a rate of 2.9% each year. What is the approximate number of customers that visit the business in 10 years
∑{t=0,9} 29600×(1-0.029)^t
= 29600 × ∑{t=0,9} (0.971)^t
= 29600×(1-(0.971)^10)/(1-0.971)
= 260212.7803191162604751275702776...
≈ 260212 (rounded down to whole person)
By ∑{i=0,n} a^i = (1-a^(n+1))/(1-a)
To find the approximate number of customers that visit the business in 10 years, we can use the formula for exponential decay:
N = N0 * (1 - r)^t
Where:
- N is the final number of customers
- N0 is the initial number of customers
- r is the rate of decline (expressed as a decimal)
- t is the number of years
Given:
N0 = 29,600 (initial number of customers)
r = 0.029 (rate of decline, expressed as a decimal)
t = 10 (number of years)
Plugging these values into the formula, we get:
N = 29,600 * (1 - 0.029)^10
Calculating this, we find:
N ≈ 29,600 * (0.971)^10 ≈ 22,773.32
Therefore, the approximate number of customers that will visit the business in 10 years is approximately 22,773.