Mathematics · May / June 2021 · Paper 31 · Question 5
YMA01
As printed in the paper
The question as text
5. log10 A (8, 0.56) (0, 0.32) O t Figure 1 The growth of duckweed on a pond is being studied. The surface area of the pond covered by duckweed, Am2, at a time t days after the start of the study is modelled by the equation A = p q t where p and q are positive constants Figure 1 shows the linear relationship between log10 A and t. The points (0, 0.32) and (8, 0.56) lie on the line as shown.
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5(a)[4]
0.56
−
0.32
log
p =
0.32
States or implies that
or
log
q
=
10
8
10
or
p =
awrt 2.089
q =
awrt 1.072
0.56
−
0.32
log
p =
0.32
States or implies that
and
log
q
=
10
10
8
and
p =
awrt 2.089
q =
awrt 1.072
5(b)[3]
States or implies that d
A
t
t =
p
ln
q
×
q
with their values for p and q
d
Rate of increase in pond weed after 6 days is 0.22 (m2/day)
(a)
0.56
−
0.32
log
p =
0.32
M1: States or implies that
or
log
q
=
or equivalent equations
10
10
8
A1: p = awrt 2.089 or q = awrt 1.072
0.56
−
0.32
log
p =
0.32
M1: States or implies that
and
log
q
or equivalent equations
=
10
10
8
A1: p = awrt 2.089 and q = awrt 1.072
(b)
M1: Uses d
≠
q
t
→
kq
t
k
1
d
t
A1: States or implies that d
A
t
t =
p
ln
q
×
q
with their values for p and q
d
A1: awrt 0.22 Units are not required
...................................................................................................................................................................................
log
0.03
0.32
Alt (b) using
A
=
t
+
as a starting point
10
M1: Attempts to differentiate and reaches 1 d
A
or equivalent
t =
k
A
d
1
d
A
A1:
t =
0.03
A
ln10 d
A1: awrt 0.22 Units are not required
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