Chang added some chlorine to the water in a pool. The chlorine evaporated at a fixed rate every week. The table below shows the amount of chlorine f(n), in ounces, that was left in the pool after n weeks:
n f(n)
1 24
2 12
3 6
4 3
Which function best shows the relationship between n and f(n)?
f(n) = 48(0.5)n − 1
f(n) = 24(0.5)n
f(n) = 24(0.5)n − 1
f(n) = 48(0.5)n + 1
To determine the relationship between n and f(n), let's analyze the table provided.
The first column represents the number of weeks (n), and the second column represents the amount of chlorine remaining in ounces (f(n)).
From the given data, we can observe that the amount of chlorine left in the pool is halved every week.
By noticing the pattern, we can conclude that the relationship between n and f(n) can be represented by the function:
f(n) = 24(0.5)^n
Therefore, the correct answer is:
f(n) = 24(0.5)^n
To determine the relationship between n (weeks) and f(n) (amount of chlorine left in the pool), let's analyze the given data:
When n = 1, f(n) = 24
When n = 2, f(n) = 12
When n = 3, f(n) = 6
When n = 4, f(n) = 3
By closely examining the values of f(n), we can see that the amount of chlorine left in the pool is halved (divided by 2) each week. This means that the amount of chlorine remaining after n weeks is related to the exponential decay function.
Since the chlorine is halved each week, we can write the function as f(n) = a(0.5)^n, where a is the initial amount of chlorine in the pool.
Now, substituting the given values into the equation, we construct the following system of equations:
24 = a(0.5)^1
12 = a(0.5)^2
6 = a(0.5)^3
3 = a(0.5)^4
Simplifying the equations, we find:
a = 48
a = 48
a = 48
a = 48
Since all the equations yield the same value for a (48), we can conclude that the initial amount of chlorine in the pool is 48 ounces.
Therefore, the function that best shows the relationship between n and f(n) is:
f(n) = 48(0.5)^n
well, each week there was 1/2 as much left, right?
online, use ^ for exponents, so it doesn't look like you're just multiplying by n
Also, use parentheses.
0.5^n - 1
is not the same as
0.5^(n-1)
So plug in a couple of values of n and see which formula works.