a. To find the number of days after which chlorine levels will reach the minimum (1.5 ppm), we need to solve the equation A(n) = 1.5.
1.5 = 2.5(0.7)^n
Dividing both sides by 2.5:
0.6 = 0.7^n
Taking the logarithm of both sides (base 0.7):
log(0.6) = log(0.7^n)
Using the logarithmic property log(a^b) = b *
log(a):
log(0.6)= n * log(0.7)
Now we can solve for n by dividing both sides by log(0.7):
n = log(0.6)/log(0.7)
Using a calculator (Desmos) to evaluate this expression, we find that n≈ 6.13. Therefore, after approximately 6.13 days, you will need to add chlorine to maintain the recommended levels.
b. The practical domain represents the valid values of n in the context of the problem. Since time (n) cannot be negative, the practical domain can be expressed as:
n≥0
c. The practical range represents the valid values of chlorine concentration (A(n)) in the context of the problem. As per the given information, the chlorine concentration should be between 1.5 and 2.5 ppm. Therefore, the practical range can be expressed as:
1.5 ≤ A(n) ≤ 2.5