Problem

Rewrite \(4\cdot~2^{t+1}\) as \(a\cdot~2^t\) so its value at \(t=0\) is visible as the leading coefficient. State that value and justify the rewrite with an exponent law.

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target=initial value; selected form=4·2t⁺¹; visible parameter=outside coefficient4; answer=f(0)=8 after evaluation; alternative less direct=8·2t actually reveals it

target=initial value; selected form=4·2t⁺¹; visible parameter=coefficient4; answer=f(0)=4; alternative less direct=none

target feature=initial value; selected form=8·2t; visible parameter=outside coefficient8; answer=f(0)=8; why alternative less direct=requires evaluating shifted exponent

target=initial value; selected form=both forms equally direct; visible parameters=4 and8; answer=f(0)=8; alternatives less direct=none

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Rewrite \(4\cdot~2^{t+1}\) as \(a\cdot~2^t\) so its value at \(t=0\) is visible as the leading coefficient. State that value and justify the rewrite with an exponent law.

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