Radioactive decay The mass of radioactive material in a sample has decreased by 30% since the decay began. Assuming a half-life of 1500 years, how long ago did the decay begin?

Population of Texas Texas was the third fastest growing state in the United States in 2016. Texas grew from 25.1 million in 2010 to 26.47 million in 2016. Use an exponential growth model to predict the population of Texas in 2025.

Savings account A savings account advertises an annual percentage yield (APY) of 5.4%, which means that the balance in the account increases at an annual growth rate of 5.4%/yr.

b. What is the doubling time of the balance?

Moore’s Law In 1965, Gordon Moore observed that the number of transistors that could be placed on an integrated circuit was approximately doubling each year, and he predicted that this trend would continue for another decade. In 1975, Moore revised the doubling time to every two years, and this prediction became known as Moore’s Law.

a. In 1979, Intel introduced the Intel 8088 processor; each of its integrated circuits contained 29,000 transistors. Use Moore’s revised doubling time to find a function y(t) that approximates the number of transistors on an integrated circuit t years after 1979.

Caffeine An adult consumes an espresso containing 75 mg of caffeine. If the caffeine has a half-life of 5.5 hours, when will the amount of caffeine in her bloodstream equal 30 mg?

Population growth The population of a large city grows exponentially with a current population of 1.3 million and a predicted population of 1.45 million 10 years from now.

b. Find the doubling time of the population.

Population growth The population of a large city grows exponentially with a current population of 1.3 million and a predicted population of 1.45 million 10 years from now.

a. Use an exponential model to estimate the population in 20 years. Assume the annual growth rate is constant.

15–20. Designing exponential growth functions Complete the following steps for the given situation.

a. Find the rate constant k and use it to devise an exponential growth function that fits the given data.

b. Answer the accompanying question.

Population The population of Clark County, Nevada, was about 2.115 million in 2015. Assuming an annual growth rate of 1.5%/yr, what will the county population be in 2025?

15–20. Designing exponential growth functions Complete the following steps for the given situation.

a. Find the rate constant k and use it to devise an exponential growth function that fits the given data.

b. Answer the accompanying question.

Savings account An initial deposit of $1500 is placed in a savings account with an APY of 3.1%. How long will it take until the balance of the account is $2500? Assume the interest rate remains constant and no additional deposits or withdrawals are made.