A container of juice is taken from the refrigerator and poured into a pitcher. The temperature of the juice will warm to room temperature over time. The temperature of the juice can be modeled by the following function: f(t)=72−32(2.718)−0.06t, where t is measured in minutes after the juice is taken out of the refrigerator. Use the drop-down menus to complete the explanation of how the function models the juice warming over time.

(1) The temperature of the juice at t = 0 is 40.

(2) 0

(3) 72

Step-by-step explanation:

The temperature of the juice can be modeled by the following function:

Here t is measured in minutes after the juice is taken out of the refrigerator.

(1)

Compute the temperature of the juice at t = 0 as follows:

Thus, the temperature of the juice at t = 0 is 40.

(2)

Compute the value of for increasing values of t as follows:

For t = 10;

For t = 20;

For t = 30;

For t = 40;

For t = 50;

For t = 60;

Thus, as time increases the value of   gets closer and closer to 0.

(3)

As the time increases the value of   gets closer and closer to 0.

This leads to f (t) getting closer and closer to 72.

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: