Question

1. paula is transferring photo files to an external hard drive to free up storage on her phone. the size of the files on her external hard drive, in megabytes, is given by f, where f = 38 + 6t, and t is the time in seconds since the transfer began. how many megabytes of files are transferred to her hard drive every second? 2. jack got home from work and turned on the air - conditioning. the temperature t (in degrees fahrenheit) of jack’s home, m minutes after turning on the air - conditioning is given by the equation t = 83 - 0.03m. a. what was the temperature of jack’s home when he first arrived? b. what will be the temperature of jack’s home after 2 hours? 3. a dairy farmer sends crates of milk to the local grocery store. the weight of the crate w, in pounds, with x jugs of milk in it is given by the equation w = 1.82 + 1.19x. a. what does the number 1.82 represent? b. what does the number 1.19 represent?

Explanation:

Step1: Analyze the first - equation

The equation for file size is $F = 38+6t$. The coefficient of $t$ represents the rate of change. So, 6 megabytes are transferred per second.

Step2: Analyze the second - equation for part a

For the temperature equation $T = 83 - 0.03m$, when $m = 0$ (just arrived), $T=83$ degrees Fahrenheit.

Step3: Analyze the second - equation for part b

First, convert 2 hours to minutes. 2 hours = 120 minutes. Substitute $m = 120$ into $T = 83-0.03m$. So, $T=83 - 0.03\times120=83 - 3.6 = 47$ degrees Fahrenheit.

Step4: Analyze the third - equation for part a

In the equation $w = 1.82+1.19x$, when $x = 0$ (no jugs of milk), $w = 1.82$. So, 1.82 is the weight of the empty crate.

Step5: Analyze the third - equation for part b

The coefficient of $x$ in $w = 1.82+1.19x$ represents the change in weight for each additional jug of milk. So, 1.19 is the weight of one jug of milk.

Answer:

1. 6 megabytes
2. a. 83 degrees Fahrenheit

b. 47 degrees Fahrenheit

1. a. The weight of the empty crate in pounds.

b. The weight of one jug of milk in pounds.