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