Question

1. the function $d(t) = 300,000t$ represents the distance (in kilometers) that light travels in $t$ seconds.

a) how far does light travel in 15 seconds?
b) how long does it take light to travel 12 million kilometers?

Explanation:

Part (a)

Step1: Identify the function and input

The function is \( d(t) = 300000t \), and we need to find \( d(15) \) (distance when \( t = 15 \) seconds).

Step2: Substitute \( t = 15 \) into the function

Substitute \( t = 15 \) into \( d(t) \): \( d(15)=300000\times15 \)

Step3: Calculate the product

\( 300000\times15 = 4500000 \)

Step1: Identify the function and known value

We know \( d(t)=12000000 \) (12 million kilometers) and the function \( d(t) = 300000t \). We need to solve for \( t \).

Step2: Set up the equation

Set \( 300000t=12000000 \)

Step3: Solve for \( t \)

Divide both sides by 300000: \( t=\frac{12000000}{300000} \)

Step4: Calculate the quotient

\( \frac{12000000}{300000}=40 \)

Answer:

For part (a), light travels \( 4500000 \) kilometers in 15 seconds.

Part (b)