Suppose that the amount, in grams, of plutonium 241 present in a given sample is determined by the function defined by $A(t)=2.00 e^{-0.053t}$, where t is measured in years. Find the amount present in the sample after the given number of years. (a) 4, (b) 10, (c) 20, (d) What was the initial amount present?

Answer each question with a vocabulary term from the Study Guide page. What are resources called that are found in limited amounts or are replaced by natural processes over extremely long periods of time?

Determine a definite integral that represents the area. determine a definite integral that represents the area $r = 3 \sin \theta$

$$5w^2-2w=0$$

Use a chart like this to list the types of sources used in each news report.

$$\begin{matrix} \text{News Report} & \text{Sources Used} & \text{ }\\ \text{"On Doomed Flight…"} & \text{ } & \text{ }\\ \text{"Memorial is Unveiled…"} & \text{ } & \text{ }\\ \end{matrix}$$

Suppose that the amount, in grams, of plutonium-$241$ present in a given sample is determined by the function

$$A(t)=2.00 e^{-0.053 t}$$

where $t$ is measured in years. Find the amount present in the sample after the given number of years. (a) $4$ (b) $10$ ($\text{}$c) $20$ (d) What was the initial amount present?

Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference and the sum of the first n terms. If the sequence is geometric, find the common ratio and the sum of the first n terms. 0, 4, 8, 12,...

For what type of assignment might you use this primary source quotation? Explain.

Evaluate dy for the given values of x and dx. y=(3+x^2)^1/2, x=1, dx=-0.1

(a) Prove that $3,5,$ and 7 are quadratic nonresidues of any Fermat prime $F_{n},$ where $n \geq 2$ (b) Show that every quadratic nonresidue of a Fermat prime $F_{n}$ is a primitive root of $F_{n}$

Order the numbers from least to greatest. $2.5,-3\frac{1}{3},\sqrt{5},-\frac{4}{5},0.\overline{75}$

A. $2.5,-3\frac{1}{3},\sqrt{5},-\frac{4}{5},0.\overline{75}$ B. $-\frac{4}{5},-3\frac{1}{3},2.5,0.\overline{75},\sqrt{5}$ C. $\sqrt{5},-\frac{4}{5},0.\overline{75},-3\frac{1}{3},2.5$ D. $-3\frac{1}{3},-\dfrac{4}{5},0.\overline{75},\sqrt{5},2.5$

Describe each step in designing a fitness program.

Mrs. Cheung hired a landscraping service to plant a row of bushes around her triangular backyard. If the bushes must be planted 3 feet apart, approximately how many bushes are needed for Mrs. Cheung's backyard?

$$a=12 \mathrm{~ft}$$

$$c=30 \mathrm{~ft}$$

Explain why an endoskeleton allows vertebrates to grow larger than animals without endoskeletons.