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?

2–9. Integrals Evaluate the following integrals.

∫₁⁴ (10^{√x} / √x) dx

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?

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.

2–9. Integrals Evaluate the following integrals.

∫ dx / √(x² − 9),x > 3

2–9. Integrals Evaluate the following integrals.

∫₀¹ (x² / (9 − x⁶)) dx

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.