Two bacterial cultures, A and B

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Two bacterial cultures, A and B, each begin with 500 cells. Culture A satisfies

\dfrac{dA}{dt}=0.03A

and culture B satisfies

\dfrac{dB}{dt}=0.07B

. Which statement is most accurate for all

t>0

? (a)

A(t)

will eventually exceed

B(t)

because the smaller growth constant leads to a larger long\-term population. (b)

\dfrac{B(t)}{A(t)}

remains constant at

\dfrac{0.07}{0.03}

for all

t

. (c)

B(t)

will exceed

A(t)

because the growth constant for

B

is larger. (d)

A(t)=B(t)

for all

t

since they begin with the same initial population and both grow exponentially.