What energy transformations occur as a skier glides down a gentle slope at constant speed?

Determine the derivatives for the given function. Assume $k$ is a constant.

$$P(t)=e^{2 t}$$

Explain why the function f and f+C, where C is a constant, have the same derivative properties.

A population grows exponentially with a proportionality constant of $1.5%.% How long will it take the population to double?

To what do the $A_1, A_3$, and $A_{\mathrm{cm}}$ temperatures refer? Are these temperatures constant?

Determine the equations of the elastic curve using the $x_1$ and $x_2$ coordinates. $E I$ is constant.

What happens to $y$ when $x$ is doubled? Here $k$ is a positive constant.

$$\frac{y}{x^4}=k$$

Using the Maclaurin series, show that if f(z) is even, its integral (with a suitable constant of integration) is odd.

Can an object have a varying speed if its velocity is constant? If yes, give examples.

Identify the constant of variation. Then write the equation of variation.

w varies inversely with z; w = -8 when z = 3.

For $d f=8$ and the constant $A$, identify the value of A such that

e. $P\left(\chi^2<A\right)=0.975$

Solve the equation, where $k$ is a positive constant.

$$3 k x^2-7 x=0$$

Use the graph to determine

$(c)$ the intervals over which the function is increasing, decreasing, and constant.

An exponential growth model is appropriate when consecutive function values appear to be changing by a constant