The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each year. What is the approximate number of customers that visit the business in 14 years?

To find the approximate number of customers that will visit the business in 14 years, we can use the formula for exponential decay:

A = P*(1 - r)^n

Where:
A = Final amount (number of customers after 14 years)
P = Initial amount (number of customers currently - 51,200)
r = Rate of decline (3.8% or 0.038 as a decimal)
n = Number of years

Substituting the given values:
A = 51,200 * (1 - 0.038)^14

To calculate this, we can break it down into steps:

Step 1: Calculate 1 - 0.038
1 - 0.038 = 0.962

Step 2: Calculate 0.962^14
You can use a calculator or a spreadsheet to calculate this exponent.

Step 3: Multiply the result from step 2 by the initial amount (51,200)
A ≈ 51,200 * (0.962^14)

After performing the calculation, we find that the approximate number of customers that will visit the business in 14 years is 33,811 (rounded to the nearest whole number).

To find the approximate number of customers that will visit the business in 14 years, we can use the formula for exponential growth/decay:

N = N₀ * (1 - r)^t

Where:
N₀ is the initial number of customers (51,200)
r is the rate of decline as a decimal (3.8% = 0.038)
t is the number of years (14)

Plugging in the values into the formula:

N = 51,200 * (1 - 0.038)^14

N ≈ 51,200 * (0.962)^14

Calculating:

N ≈ 51,200 * 0.528344

N ≈ 27,055.41

Therefore, the approximate number of customers that will visit the business in 14 years is around 27,055.