U.S. Population The Museum of Science in Boston displays a running total of the U.S. population. On May $11, 1993.$ the toxal was increasing at the rate of $1$ person every $14$ sec. The displayed population figure at $3:45$ P.M. that day was $257,313,431$. Assume that the relative growth rate is constant.
What is the relative growth rate per year ( $365$ days)?

Evaluate the integral analytically. Support your answer using NINT.

$$\displaystyle\int_0^{\pi / 2} x^2 \sin 2 x d x$$

John Napier (1550-1617), the Scottish laird who invented logarithms, was the first person to answer the question, "What happens if you invest an amount of money at 100% yearly interest, compounded continuously?" How long does it take to triple your money?

John Napier (1550 - 1617), the Scottish laird who invented logarithms, was the first person to answer the question, "What happens if you invest an amount of money at 100% yearly interest, compounded continuously?"

Evaluate the integral.

$$\displaystyle\int \frac{d x}{x \ln x}$$

Use substitution to evaluate the integral.

$$\displaystyle\int \cos (3 z+4) d z$$

Find the exponential function $y=y_0 e^{k t}$ whose graph passes through the two points.

Points$(0,2),(2,5)$

The number of radioactive atoms remaining after t days in a sample of polonium-210 that starts with yₒ radioactive atoms is y = yₒeˉ⁰∙⁰⁰⁵ᵗ . Your sample will not be useful to you after 95% of the radioactive nuclei present on the day the sample arrives have disintegrated. For about how many days after the sample arrives will you be able to use the polonium?

A population function is given. Estimate P(0). Explain its meaning in the context of the problem. The number of students infected by measles in a certain school is given by the formula P(t) = 200/1+e⁵·³ ˉ ͭ , where t is the number of days after students are first exposed to an infected student.

The number of students infected by measles in a certain school is givern by the formula P(t) = 200/1+e⁵·³ ˉ ͭ where t is the number of days after students are first exposed to the infected student..

The number of radioactive atoms remaining after t days in a sample of polonium-210 that starts with yₒ radioactive atoms is y = yₒeˉº·ºº⁵ᵗ. Find the element's half-life.

Use substitution to evaluate the integral.
$\displaystyle\int_{-\pi / 4}^{\pi / 4} \tan ^2 x \sec ^2 x d x$

Evaluate the integral.

$$\displaystyle\int e^x \sec (e^x) d x$$

Evaluate the integral. \

$$\displaystyle\int(3 \sin x-\sin 3 x) d x$$