Problem

Assume an unshifted exponential family through \((0,~12)\) and \((3,~96)\). Determine and verify the model, predict \(f(4)\), classify the prediction as interpolation or extrapolation, and state both the family and continuation assumptions.

Answer choices

Choose your path.

Preview only

model = f(x)=12·2ˣ with initial 12 and base 2; verification = f(0)=12 and f(3)=96; prediction = f(4)=192; type = interpolation because 4 is near 3; assumption = no family assumption is needed

model = f(x)=12·8ˣ with initial 12 and base 8; verification = f(0)=12 and f(3)=6144; prediction = f(4)=49152; type = extrapolation; assumption = 96/12 is one-step base

model = f(x)=28x+12 with slope 28; verification = f(0)=12 and f(3)=96; prediction = f(4)=124; type = extrapolation; assumption = two points make linear impossible

model = f(x)=12·2ˣ with initial 12 and base 2; verification = f(0)=12 and f(3)=96; prediction = f(4)=192; type = extrapolation beyond [0,3]; assumption = factor 2 continues and two points alone do not prove exponential family

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Assume an unshifted exponential family through \((0,~12)\) and \((3,~96)\). Determine and verify the model, predict \(f(4)\), classify the prediction as interpolation or extrapolation, and state both the family and continuation assumptions.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.