Solve the problem.
-Hi-Tech UnWater begins a cable TV advertising campaign in Miami to market a new water. The percentage of the target market that buys water is estimated by the function t represents the number
Of days of the campaign. After how long will 90% of the target market have bought the water?
A) 90 days
B) 115 days
C) 120 days
D) 3 days

Question

Solve the problem.
-Hi-Tech UnWater begins a cable TV advertising campaign in Miami to market a new water. The percentage of the target market that buys water is estimated by the function  t represents the number
Of days of the campaign. After how long will 90% of the target market have bought the water?
A) 90 days 
B) 115 days 
C) 120 days 
D) 3 days

Quizplus · Accepted Answer

To find out after how long 90% of the target market have bought the water, we need to solve the equation: 
0.9 = 100 / (1 + e^-0.03t)
Multiplying both sides by (1 + e^-0.03t) gives: 
0.9 + 0.9e^-0.03t = 100
Subtracting 0.9 from both sides gives: 
0.9e^-0.03t = 99.1
Dividing both sides by 0.9 gives: 
e^-0.03t = 110.11
Taking the natural logarithm of both sides gives: 
-0.03t = ln(110.11)
Dividing both sides by -0.03 gives: 
t ≈ 115.08
Therefore, after approx. 115 days, 90% of the target market will have bought the water.

Solve the Problem. -Hi-Tech UnWater Begins a Cable TV Advertising Campaign in Miami