Question

A dietician recommends that a patient increase the daily caloric intake of
1,045 calories by 5% each day,x, until the patient has a new daily caloric intake of at least y calories. Which system of inequalities represents the scenario

Answer 1

Using an exponential function, it is found that the inequalities that represents the scenario is:

$y \geq 1045(1.05)^x$

$x \geq 0$

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^t$

In which:

• A(0) is the initial value.

• r is the growth rate, as a decimal.

In this problem:

• Initial daily caloric intake of 1,045 calories, hence A(0) = 1045.

• Increased by 5%, hence r = 0.05.

We want a new daily caloric intake of at least y calories, hence:

$y \geq 1045(1.05)^x$

The number of days is at least 0, hence:

$x \geq 0$

More can be learned about exponential functions at https://brainly.com/question/25537936