MathDB
Problems
Contests
National and Regional Contests
Germany Contests
German National Olympiad
1962 German National Olympiad
1
1
Part of
1962 German National Olympiad
Problems
(1)
y = a - b 10^{-kx}
Source: 1961-62 Germany R4 12.1
10/12/2024
In 27,000 fertilization trials with phosphorus fertilizers, the following average average crop yields for potatoes were found:
F
e
r
t
i
l
i
z
e
r
a
p
p
l
i
c
a
t
i
o
n
b
a
s
e
d
o
n
P
2
O
5
(
d
t
/
h
a
)
′
c
r
o
p
y
i
e
l
d
(
d
t
/
h
a
)
Fertilizer \,\, application \,\,based \,\,on \,\,P2O5 (dt/ha) \ '\ crop \,\, yield \,\, (dt/ha)
F
er
t
i
l
i
zer
a
ppl
i
c
a
t
i
o
n
ba
se
d
o
n
P
2
O
5
(
d
t
/
ha
)
′
cro
p
y
i
e
l
d
(
d
t
/
ha
)
0.0
237
0.0 \ \ 237
0.0
237
0.3
251
0.3 \ \ 251
0.3
251
0.9
269
0.9 \ \ 269
0.9
269
The relationship between the fertilizer application
x
x
x
(in dt/ha) and the crop yield
y
y
y
(in dt/ha), can be approximated by the following relation:
y
=
a
−
b
⋅
1
0
−
k
x
y = a - b \cdot 10^{-kx}
y
=
a
−
b
⋅
1
0
−
k
x
where
a
,
b
a, b
a
,
b
and
k
k
k
are constants. a) Calculate these constants using the values given above! b) Calculate the crop yield for a fertilizer application of
0.6
0.6
0.6
dt/ha and
1.2
1.2
1.2
dt/ha! c) Set the percentage deviation of the calculated values from those determined in the experiment values
261
261
261
dt/ha or
275
275
275
dt/ha.
algebra