If h(t) is a person's heart rate in beats per minute t minutes into an exercise session, what does

$$\int_{0}^{30} h(t) d t$$

represent?

Develop an explicit formula for the toothpick sequence using the first term and the common difference. The first term of the sequence is $a_{1}=8$. The second term is $a_2 = 8 + 6$. The third term is $a_3 = 8 + 6 + 6$, or $a_3 = 8 + 2(6).$ a. Write an expression for the fourth term using the value of $a_1$ and the common difference. $a_4= ?$ b. Express regularity in repeated reasoning. Use the patterns you have observed to determine the 15th term. Justify your reasoning. $a_{15} = ?$ c. Write an expression that can be used to find the nth term of the toothpick sequence. $a_n= ?$

$\text{\blue{WHAT IF?}}$ What evolutionary processes might account for prokaryotes having smaller genomes than eukaryotes?

We defined the marginal revenue function $R^{\prime}(x)$ as the derivative of the revenue function $R(x)$, where x is the number of units sold. What does $\int_{1000}^{5000} R^{\prime}(x) d x$ represent?

The function $f(x)=2.5 x+3.5$ gives the $\operatorname{cost} f(x)$ of a cab ride of x miles. What is the cost of a 6-mile ride?

$$\text{\blue{EVOLUTION CONNECTION}}$$

What evolutionary mechanisms might account for the origin and persistence of cell-to-cell signaling systems in unicellular prokaryotes?

What evolutionary mechanisms might account for the origin and persistence of cell-to-cell signaling systems in prokaryotes?

If oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does ∫120 0 r(t) dt represent?

Set up, but do not evaluate, an integral representing the area of the region enclosed by the given curves.

$$y=2^{x}, \quad y=3^{x}, \quad x=1$$

If oil leaks from a tank at a rate of $r(t)$ gallons per minute at time $t$, what does $\int_0^{120} r(t)~dt$ represent?

If $w'(t)$ is the rate of growth of a child in pounds per year, what does $\int_5^{10} w'(t)~dt$ represent?

Escribe la forma correcta del verbo ser para completar lo que Alejandro escribe sobre los estudiantes en su clase de español. Pero a mí no me gusta ir al gimnasio porque no _____ deportista.

You can use the coefficients of this form of an equation to find the x-intercept, y-intercept, and slope. a. Determine the x-intercept. b. Determine the y-intercept. c. Write $Ax+ By= C$ in slope-intercept form to find the slope.

Evaluate the integral.

$$\int \frac{e^{x}}{1+e^{2 a}} d x$$