Population growth model to solve for various things

1.This exercise uses the population growth model.

A certain culture of the bacterium Rhodobacter sphaeroides initially

has 45 bacteria
and is observed to double

every 6 hours.

(a) Find an exponential model n(t) = n₀2^t/a for the number of bacteria in the culture after t hours.

(b) Estimate the number of bacteria after 14 hours. (Round your answer to the nearest whole number.)

(c) After how many hours will the bacteria count reach 1 million? (Round your answer to one decimal place.)

2.This exercise uses the population growth model.

A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 26,000.

(a) What was the initial size of the bird population? (Round your answer to the nearest whole number.)

(b) Estimate the bird population 3 years from now. (Round your answer to the nearest whole number.)

3. This exercise uses the radioactive decay model.

The half-life of cesium-137 is 30 years. Suppose we have a 12-g sample.

(a) Find a function m(t) = m₀2^−t/h that models the mass remaining after t years.

(b) Find a function m(t) = m₀e^−rt that models the mass remaining after t years. (Round your r value to four decimal places.)

(c) How much of the sample will remain after 78 years? (Round your answer to one decimal place.)

d) After how many years will only 4 g of the sample remain? (Round your answer to the nearest whole number.)