Question

1 kilogram (kg) is about 2.2 times as heavy as 1 pound (lb). Suppose the function f determines Emanuel's weight (in lbs), f ( t ) , given the number of days t since the beginning of 2017. The function g determines Emanuel's weight (in kg), g ( t ) , given the number of days t since the beginning of 2017. a Suppose f(35) 171. What is the value of g(35)?b. Write a formula for g using the function f.

Answer 1

Answer:

(a) The value g(35) is 77.727.

(b) The required function for g(t) is g(t)=2.2f(t).

Step-by-step explanation:

(a)

It is given that 1 kilogram (kg) is about 2.2 times as heavy as 1 pound (lb).

1 kg = 2.2 lbs              .... (1)

The function f(t) determines Emanuel's weight (in lbs) and function g(t) determines Emanuel's weight (in kg), where t is the number of days since the beginning of 2017.

It is given that f(35)=171, it means the Emanuel's weight is 171 lbs after 35 days since the beginning of 2017.

We have to find the value of g(35). So, we need to find Emanuel's weight in kg after 35 days since the beginning of 2017.

$1\text{ kg }=2.2\text{ lbs}$

Divide both sides by 2.2.

$\frac{1}{2.2}\text{ kg }=1\text{ lbs}$

Multiply both sides by 171.

$\frac{171}{2.2}\text{ kg }=171\text{ lbs}$

$77.727\text{ kg }=171\text{ lbs}$

Therefore the value g(35) is 77.727.

(b)

Since f(t) is Emanuel's weight (in lbs) and g(t) is Emanuel's weight (in kg), therefore using conversion (1) we get

$g(t)=2.2\times f(t)$

$g(t)=2.2f(t)$

Therefore the required function for g(t) is g(t)=2.2f(t).