Question 1

Paper 2, calculatorMedium6 marks

A capacitor is discharged from an initial voltage of 10 V. Its voltage VV in volts, tt seconds after discharge is modelled by

V(t)=10at,t≥0,V(t)=10a^t,\qquad t\geq 0,

where 0<a<10<a<1 After 4 seconds, the voltage is 6.4 V.

(a)

Determine the value of aa correct to three significant figures.

[1]
(b)

Let T(V)T(V) give the time, in seconds, at which the voltage is VV Determine T(V)T(V) stating its domain.

[2]
(c)

Hence determine the time at which the model predicts the voltage is 2.5 V. State whether the model predicts that the voltage reaches 0 V at any finite time, and justify your answer.

[3]

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