Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 12.5, 2.5, 0.5, 0.1, 0.02.
Which exponential function is represented by the table?

f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)

Answer 1

f(0)=0.5, so the coefficient is 0.5. The common ratio is f(1)/f(0)=0.1/0.5=0.2, so the base is 0.2. Thus the function is f(x) = 0.5(0.2^x).