Rational Exponents Assignment

Distance from the sun (au) Orbital Period (years)

.....

Mercury

0.39 0.242

Venus

0.72 0.616

Earth

1 1

A power regression equation for this data is: T = A^

1.5

Mars

1.52 1.88

You used a telescope and other mathematics to discover that Jupiter is 5.20 au from the sun. Use the equation to find its orbital period. Round to the nearest tenth of a year. Jupiter's Orbit: years

11.9

Uranus

19.18 84.0

Neptune

30.06 165

Jupiter

5.20 N/A

Suppose that your data shows that Saturn orbits every 29.5 years. To the nearest hundredth of an au, how far is Saturn from the Sun?Saturn's Distance from the Sun: au

9.55

The equation T = A3/2 is great if you know A and want to find T.Now, identify the correct inverse equation, which can be used to find A when you are given T.

A = T2/3

Convert the equation you found, T = A3/2, into a form without any rational exponents.

C T2=A3

Saturn

N/A 29.5

Use the fact that 1.5 is the same as 3/2 to select all of the equations below that are equivalent toT = A1.5.

T = A3/2 T = (A1/2)3 (all four options)

Mercury and Venus are the sun than Earth is.

closer to

The further a planet is from the sun, the its orbit is.

longer

So, their orbital periods are than Earth's orbit.

shorter

Translate the answer, T2 = A3, into words:The squaresquare rootcube of the orbital period, T, of a planet is equal to the squaresquare rootcube of the average distance, A, of the planet from the Sun.

square cube