A simple technique that biologists use to estimate the age of an African elephant is to measure the length of the elephant's footprint and then calculate its age using the equation,

l = 45 - 25.7e ^-0.09a

where k is the length of the footprint and a is the age (in years).

a) Use the equation to find the ages of the elephants whose footprints are given.

1) 36cm

2) 32cm

3) 28cm

4) 24cm

b) Solve the equation for a, and use this equation to find the ages of the elephants whose footprints are given.

c) Compare the methods you used in parts (a) and (b). Which method do you prefer? Explain?

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

Step-by-step 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.