Answer:
1) 36 cm a = 11.65 years
2) 32 cm a = 7.57 years
3) 28 cm a = 4.59 years
4) 24 cm a = 2.24 years
Explanation:
Estimating the age of an African elephant by length of the elephant's footprint.
k = 45 - 25.7e^-0.09a
Where a is the age in years and k is length of the footprint
a) Use the equation to find the ages of the elephants whose footprints are given.
1) 36 cm
36 = 45 - 25.7e^-0.09a
36 - 45 = - 25.7e^-0.09a
-9 = - 25.7e^-0.09a
divide both side by -25
-9/-25.7 = - 25.7e^-0.09a/-25.7
0.3502 = e^-0.09a
take log on both sides
ln(0.3502) = ln(25e^-0.09a)
we know that ln(e^a = a ln(e)
ln(0.3502) = -0.09a*ln(e)
we know that ln(e) = 1
ln(0.3502) = -0.09a
a = ln(0.3502)/-0.09
a = -1.049/-0.09
a = 11.65 years
Similiarly, we repeat the above procedure to find the remaining ages for the given length of footprints
2) 32 cm
32-45/-25.7=e^-0.09a
ln(0.5058) = -0.09a
a = ln(0.5058)/-0.09
a = 7.57 years
3) 28 cm
28-45/-25.7=e^-0.09a
ln(0.6614) = -0.09a
a = ln(0.6614)/-0.09
a = 4.59 years
4) 24 cm
32-45/-25.7=e^-0.09a
ln(0.8171) = -0.09a
a = ln(0.8171)/-0.09
a = 2.24 years
b)Solve the equation for a, and use this equation to find the ages of the elephants whose footprints are given.
we have to make a the subject of the equation
k = 45 - 25.7e^-0.09a
k - 45 = -25.7e^-0.09a
k - 45/-25.7 = e^-0.09a
ln(k - 45/-25.7) = ln(e^-0.09a)
ln(k - 45/-25.7) = -0.09aln(e)
ln(k - 45/-25.7) = -0.09a
a = ln(k - 45/-25.7)/-0.09
Now we just have to plug the value of k and we get age
1) 36 cm
a = ln(36 - 45/-25.7)/-0.09
a = 11.65 years
2) 32 cm
a = ln(36 - 45/-25.7)/-0.09
a = 7.57 years
3) 28 cm
a = ln(36 - 45/-25.7)/-0.09
a = 4.59 years
4) 24 cm
a = ln(36 - 45/-25.7)/-0.09
a = 2.24 years
c) Compare the methods you used in parts (a) and (b). Which method do you prefer? Explain?
Well, obviously I would prefer part (b). part (b) method is better than part (a) because of the less number of steps involved. So if there are repeated calculations like in this problem where we have to calculate age for 4 different footprints then part (b) method would save us a lot of time.