The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
An equation is an expression that shows the relationship between two or more variables and numbers.
For the exponential function, when f(2) = 12:
12 = ab² (1)
Also, at f(4) = 48:
48 = ab⁴ (2)
Hence:
a = 3, b = 2
f(x) = 3(2)ˣ
For the linear function using the points (2, 12) and (4, 48):
y - 12 = [(48 - 12) / (4 - 2)](x - 2)
y = 18x - 24
The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively
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