Use exponent properties to interpret exponential expressions, including percent growth and decay.
Choose the equivalent exponential form that makes the requested feature easiest to read
Problem
Rewrite \(5(2)^{t+3}\) in the equivalent form \(a(2)^t\) that makes the value at \(t=0\) visible as \(a\). Use \(2^{t+3}=2^t\cdot~2^{3}\), combine constants, and verify by substituting \(t=0\) in both forms.
Big Picture
What this problem is really about
Equivalent exponential forms can reveal different features of the same function. We’ll rewrite the variable exponent to be exactly the input, absorb the fixed power into the coefficient, and verify at input zero that the new coefficient exposes the initial value.
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