How do you estimate the instantaneous rate of change for which the door is moving at #t=1# second if the equation for an automatic door is #d=200t * 2^(-t)#?

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How do you estimate the instantaneous rate of change for which the door is moving at #t=1# second if the equation for an automatic door is #d=200t * 2^(-t)#?

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Answer 1 · 2015-03-28T01:58:38

Derive your equation (to get the instantaneous rate of change) and set #t=1# in the derivative:
#d'(t)=200*2^-t+200t[-2^-t(ln2)]#
for #t=1#
#d'(1)=200/2+200[-ln(2)/2]=200/2[1-ln(2)]~=30.7#

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How do you estimate the instantaneous rate of change for which the door is moving at #t=1# second if the equation for an automatic door is #d=200t * 2^(-t)#?

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