Question

The Baker family started a farm in 1900, and the farm has been passed down from generation to generation. The Bakers primarily produce corn and potatoes on their farm. The following equation models the number of pounds of corn they produced each year t years after 1900.

C(t) = 25,000 + 500 ln(t + 1)

The graph below models the number of pounds of potatoes they produced each year t years after 1900.

Which of the following statements best describes the quantity of corn and potatoes produced as time passed?

A.) The Baker family has always and will always produce more potatoes than corn.

B.) The Baker family has always and will always produce more corn than potatoes.

C.) The Baker family started off producing more corn than potatoes, but as time passed, they eventually produced more potatoes than corn.

D.) The Baker family started off producing more potatoes than corn, but as time passed, they eventually produced more corn than potatoes.

Answer 1

Answer: it’s A for Plato users!

Answer 2

we have that

The following equation models the number of pounds of corn they produced each year t years after 1900.

C(t) = 25,000 + 500 ln(t + 1)

using a graph tool

see the attached figure N 1

for t=0 (year 1900)

C=25,000 pounds of corn

for t=100 (year 2000)

C=27,308 pounds of corn---->see the attached figure N 2

pounds of potatoes

for t=0 (year 1900)

P=30,000 pounds of potatoes----> see the given graph

for t=100 (year 2000)

P < 24,000 pounds of potatoes------> see the given graph

therefore

the answer is the option

D.) The Baker family started off producing more potatoes than corn, but as time passed, they eventually produced more corn than potatoes.