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

$$y=\frac{k}{x^3}$$

Solve the equation for the indicated variable.

$10\left(r^2-4\right)=18$; for $r$

In the following Exercise, write the expression in the form $k x^p$. Give the values of k and p.

$3 \sqrt{x}$

Solve the equation for the variable.

$$2 x^2=8.6$$

The circulation time of a mammal (that is, the average time it takes for all the blood in the body to circulate once and return to the heart) is proportional to the fourth root of the body mass of the mammal.

(a) Write a formula for the circulation time, $T$, in terms of the body mass, $B$.

(b) If an elephant of body mass 5230 kilograms has a circulation time of 148 seconds, find the constant of proportionality.

(c) What is the circulation time of a human with body mass 70 kilograms?

Without solving them, say whether the equation $x^5=3$ have

(i) One positive solution

(ii) One negative solution

(iii) One solution at $x=0$ (iv) Two solutions

(v) Three solutions

(vi) No solution

Give a reason for your answer.

In the following Exercise, a pair of power functions having the same coefficients but different exponents is given. In the long run, which function in the pair dominates?

$f(x)=350 x^{0.081}$ and $g(x)=350 x^{0.09}$

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

$$y=k x^3$$

In this Exercise, a and b are positive numbers and a>b. Which is larger, f(a) or f(b) ?

$$f(t)=\frac{\sqrt{5}}{t^7}$$

Write a formula representing the function.

The radius, $r$, of a circle is proportional to the square root of the area, $A$.

Solve the equation for the indicated variable.

$4(s+3)-7(s+10)=25$; for $s$

Solve the equation for the variable.

$$(x+1)^2+4=29$$

Solve the equation for the indicated variable.

$5 x^2=32$; for $x$

In the following Problem, a and b are positive numbers. If $a>b$ then which is larger?

$$3^a, 3^b$$