The table shows the projected number of visitors (in thousands) at a zoo.
year
1
2
3
4
zoo visitors (thousands)
64
32
16
8
An equation, f(x) , for the projected number of zoo visitors (in thousands) in year x can be represented by f(x)=a(b)^x where a ≠0 and b >0. Construct the equation.
f(x)=[blank](blank)^x
3 answers
f(x)=64(0.5)^x
its 128
Apologies for the mistake. Let's correct that.
The initial number of visitors in year 1 is 64, so f(1) = 64. This gives us the equation:
f(1) = a(b)^1 = 64
a(b) = 64
In year 2, the number of visitors is 32, so f(2) = 32:
f(2) = a(b)^2 = 32
Dividing the equation for year 2 by the equation for year 1:
32 = a(b)^2
64 = a(b)
Dividing the second equation by the first equation:
64 = 2b
So, b = 32
Substitute b back into the equation a(b) = 64:
a(32) = 64
a = 2
Therefore, the equation is:
f(x) = 2(32)^x
The initial number of visitors in year 1 is 64, so f(1) = 64. This gives us the equation:
f(1) = a(b)^1 = 64
a(b) = 64
In year 2, the number of visitors is 32, so f(2) = 32:
f(2) = a(b)^2 = 32
Dividing the equation for year 2 by the equation for year 1:
32 = a(b)^2
64 = a(b)
Dividing the second equation by the first equation:
64 = 2b
So, b = 32
Substitute b back into the equation a(b) = 64:
a(32) = 64
a = 2
Therefore, the equation is:
f(x) = 2(32)^x
1 answer