I'm not getting anywhere?
I have to do the exercises below. Can someone who's good at math help me? Please.
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actually quite simple, you just have to use the right things in the equation.
for example b: x should represent the years, the relative y the cm that grow this year. That means we are
y=90*0.87^10 after 10 years.
Turned around at c, it is asked for 50cm:
50 = 90*0.87^x
(a)
The half-life is obtained by the batch
0.87^x = 0.5
Solution:
ln (0.87^x ) = ln ( 0.5 )
x*ln (0.87 ) = ln ( 0.5 )
x = ln ( 0.5 ) / ln ( 0.87 ) ~ 4.97729 years
Meaning: within approx. 5 years, the rate of growth drops around the holdings.
(b)
f(10) = 90*0.87^10 ~ 22.36 cm
(c)
Approach:
90*0.87^x = 50
Solution:
ln(90*0.87^x ) = ln (50 )
ln(90) + ln(0.87^x ) = ln (50 )
ln(90) + x*ln(0.87 ) = ln (50 )
x = (ln (50) – ln(90))/ln(0.87) ~ 4.22072 years
(d)
F(x)= -90/(ln(100)-ln(87)) * 0.87^x + C
(e)
F(10) – F(0) ~ 485.72 cm
Meaning: within approx. 10 years the tree has grown by 485.71 cm in addition to the 90 cm at the beginning.
(f)
F(20) – F(0) ~ 606.38 + 90 cm
G)
(F(20) – F(0) ) / 20 ~ 32.76 cm / year