Question

1 kilogram (kg) is about 2.2 times as heavy as 1 pound (lb). Suppose the function f determines Marcus's weight (in lbs), f ( t ) , given the number of days t since the beginning of 2017. The function g determines Marcus's weight (in kg), g ( t ) , given the number of days t since the beginning of 2017. Suppose f ( 29 ) = 194 . What is the value of g ( 29 ) ? g ( 29 ) = Write a formula for g using the function f .

Answer 1

1. g(29)=88.18

2.
`g(t)=(f(t))/(2.2)`

Explanation:

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

1 kg = 2.2 lb

Let as consider f determines Marcus's weight (in lbs), f ( t ) , given the number of days t since the beginning of 2017.

The function g determines Marcus's weight (in kg), g ( t ) , given the number of days t since the beginning of 2017.

It is given that f ( 29 ) = 194, it means the 29 Marcus's weight (in lbs) is 194.

Using the above conversion we get

`1\text{ lb }=(1)/(2.2)\text{ kg}`

Multiply both sides by 194.

`194* 1\text{ lb }=194* (1)/(2.2)\text{ kg}`

`194\text{ lb }=88.181818\text{ kg}`

It means the 29 Marcus's weight (in kg) is about 88.18.

`g(29)=88.18`

Since 1 kg = 2.2 lb, it means weight in kg must be multiplied by 2.2 to convert it into lbs.

`g(t)* 2.2=f(t)`

Divide both sides by 2.2.

`g(t)=(f(t))/(2.2)`

Therefore the formula for g using the function f is
`g(t)=(f(t))/(2.2)`.