Use exponent properties to interpret exponential expressions, including percent growth and decay.
Rewrite an exponential expression with a shifted exponent to show the initial value at t = 0
Problem
Rewrite \(8(2)^{t+2}\) in the form \(a(2)^t\) so the value at \(t=0\) is explicit. Split \(2^{t+2}\) into \(2^t\cdot~2^{2}\), combine the constant factors, and verify the result by substituting \(t=0\).
Big Picture
What this problem is really about
A shift in the exponent hides a constant power of the base inside the expression. We’ll split the exponent sum into variable and constant powers, combine the constant power with the outside coefficient, and evaluate at input zero to verify the exposed initial value.
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