# Calculations Shown

A certain culture of the bacterium Streptococcus A initially has 10 bacteria and is observed to double every 1.5 hours.

(a) Find an exponential model

(b) Estimate the number of bacteria after 34 hours. (Round your answer to the nearest whole number.)

(c) After how many hours will the bacteria count reach 10,000? (Round your answer to one decimal place.)

The fox population in a certain region has a relative growth rate of 8% per year. It is estimated that the population in 2013 was 16,000.

(a) Find a function

(b) Use the function from part (a) to estimate the fox population in the year 2019. (Round your answer to the nearest whole number.)

(c) After how many years will the fox population reach 24,000? (Round your answer to one decimal place.)

The population of a country has a relative growth rate of 2% per year. The government is trying to reduce the growth rate to 1%. The population in 2011 was approximately 120 million. Find the projected population for the year 2040 for the following conditions. (Round your answers to the nearest whole number.)

(a) The relative growth rate remains at 2% per year.

(b) The relative growth rate is reduced to 1% per year.
The count in a culture of bacteria was 200 after 2 hours and 12,800 after 6 hours.

(a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.)

(b) What was the initial size of the culture? (Round your answer to the nearest whole number.)

(c) Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form

n0e^rt.

Round your n0 value to the nearest whole number. Round your r value to two decimal places.)

n(t) = _______

(d) Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.)

e) After how many hours will the number of bacteria reach 25,000? (Round your answer to two decimal places.)

The half-life of radium-226 is 1600 years. Suppose we have a 24-mg sample.

(a) Find a function

m(t) = m02^−t/h

that models the mass remaining after t years.

m(t) = ____________

(b) Find a function

(c) How much of the sample will remain after 3500 years? (Round your answer to one decimal place.)

(d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.)