While cramming for her MAT all find / exerminationSibalive learns a large number of proofs. At a timeI weeks after the examination, the percentage of thoseproofs she is able to recall is given by the formulap(t) = 180 + 20e1+ €0.5tAccording to this formulela) the percentage of proces she is able to recall atothe time of writing the examination isby the percentage of proofsFour weeks after writing(1)E₂a how many weeks after the examination will Sibaliwe beable to receill exactly 40% of the proofs?d) Applying Four iterations of the interval halvinelamethod to F(t) = pct) - 40, taking the initialapproximations t₁ = 3 and ta = 5, yield the followingapprexinations for the number of weeks after whichSibaline is able to recall exactly 40% of the proofsshe memorized for the examinationand to² =(21t30.5t(3)2167.90==she is able to recelllthe examination isAltS

Answered: examination roofs. At a time ercentage…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

While cramming for her MAT all find / exermination
Sibalive learns a large number of proofs. At a time
I weeks after the examination, the percentage of those
proofs she is able to recall is given by the formula
p(t) = 180 + 20e
1+ €0.5t
According to this formulel
a) the percentage of proces she is able to recall ato
the time of writing the examination is
by the percentage of proofs
Four weeks after writing
(1)
E₂
a how many weeks after the examination will Sibaliwe be
able to receill exactly 40% of the proofs?
d) Applying Four iterations of the interval halvinela
method to F(t) = pct) - 40, taking the initial
approximations t₁ = 3 and ta = 5, yield the following
apprexinations for the number of weeks after which
Sibaline is able to recall exactly 40% of the proofs
she memorized for the examination
and to² =
(21
t3
0.5t
(3)
2167.90
=
=
she is able to recelll
the examination is
Alt
S

Expert Solution

Step 1

# As per the guidelines we are entitled to solve one three subparts at a time, please resubmit the other parts if you wish to get them answered.

Given that $p (t) = \frac{180 + 20 e^{0.5 t}}{1 + e^{0.5 t}}$ where t is the number of weeks after examination and p(t) is the percentage of proofs Sibaliwe is able to recall.

(a)

The percentage of proofs she is able to recall at the time of writing the examination is given by substituting t=0 in the given formula.

$\begin{array}{rcl} p (0) & = & \frac{180 + 20 e^{0.5 (0)}}{1 + e^{0.5 (0)}} \\ = & \frac{180 + 20 e^{0}}{1 + e^{0}} \\ = & \frac{180 + 20}{1 + 1} \\ = & \frac{200}{2} \\ = & 100 \end{array}$