MATH SOLVE

2 months ago

Q:
# the number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time t=0 , which of the following expressions gives the number of bacteria in the container at time t=3 hours?

Accepted Solution

A:

The number of bacteria will modeled using exponential growth function, this is given by:

f(x)=a(b)^x

where

a is the initial amount

b=ratio of growth

x=time

Thus from our information we shall have:

f(x)=R(t)

a=1000

b=r

t=x

hence we shall model the situation by:

R(x)=1000(r)^t

Hence in 3 years time the population will be modeled by the function:

R(x)=1000(r)^3=1000rΒ³

f(x)=a(b)^x

where

a is the initial amount

b=ratio of growth

x=time

Thus from our information we shall have:

f(x)=R(t)

a=1000

b=r

t=x

hence we shall model the situation by:

R(x)=1000(r)^t

Hence in 3 years time the population will be modeled by the function:

R(x)=1000(r)^3=1000rΒ³