Question

1. the function $d(t) = 300000t$ represents the distance that light travels in $t$ seconds.

a. how far does light travel in 15 seconds?

b. how long does it take light to travel 12,000,000 kilometers?

Explanation:

Part a

Step 1: Identify the function and input

We have the distance function \( d(t)=300000t \), and we need to find the distance when \( t = 15 \) seconds.

Step 2: Substitute \( t = 15 \) into the function

Substitute \( t = 15 \) into \( d(t)=300000t \), we get \( d(15)=300000\times15 \).

Step 3: Calculate the result

\( 300000\times15 = 4500000 \)

Step 1: Identify the function and the distance

We know \( d(t)=300000t \), and we are given that \( d(t)=12000000 \) kilometers. We need to find \( t \).

Step 2: Set up the equation

Set \( 300000t=12000000 \).

Step 3: Solve for \( t \)

Divide both sides of the equation by 300000: \( t=\frac{12000000}{300000} \).

Step 4: Calculate the result

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

Answer:

Light travels \( 4500000 \) kilometers in 15 seconds.

Part b