Question

Sandi tracks her calories burned during water aerobics class. The number of calories she burns is expressed by the function c(t) = 350t, where t is the number of hours spent doing water aerobics.

To burn more calories, Sandi wears ankle weights during her class. The number of calories she burns while wearing ankle weights is expressed by the function b(c) = 1.2c, where c is the number of calories burned doing water aerobics without weights.

Which of the following composite functions expresses the calories, as a function of time, Sandi burns while doing water aerobics with ankle weights?

Answer 1

Answer:

$b[c(t)] =420t$

Step-by-step explanation:

As per the statement:

The number of calories she burns is expressed by the function:

$c(t) = 350t$

where, t is the number of hours spent doing water aerobics.

To burn more calories, Sandi wears ankle weights during her class.

The number of calories she burns while wearing ankle weights is expressed by the function:

$b(c) = 1.2c$

where, c is the number of calories burned doing water aerobics without weights.

We have to find the calories, as a function of time, Sandi burns while doing water aerobics with ankle weights i.e $b[c(t)]$

Given:

$b(c) = 1.2c$

Replace c with c(t) we have;

$b[c(t)] = 1.2(c(t))$

Substitute the value of c(t) = 350t we get;

$b[c(t)] = 1.2 \cdot 350t$

Simplify:

$b[c(t)] =420t$

Therefore, the the following composite functions expresses the calories, as a function of time, Sandi burns while doing water aerobics with ankle weights is, $b[c(t)] =420t$

Answer 2

Answer:

b[c(t)] = 420t

Step-by-step explanation:

Number of calories burnt by Sandi is expressed by the function c(t) = 350t

where t = number of hours spent doing water aerobics.

Similarly number of calories burnt while wearing ankle weights, by the function b(c) = 1.2c

where c = number of calories burnt

Now, function that represents the calories as a function of time will be

b[c(t)] = 1.2(350t)

         = 420t

Therefore, composite function representing calories burnt as function of time will be b[c(t)] = 420t