Chapter 6.3, Problem 32E

To determine

Tofind: A function that models the given data.

Answer to Problem 32E

We choose the model using exponential regression initially injected $20.36$ milligrams into the animal’s body.

Explanation of Solution

Given information :

Table shows amount, $a$ (in milligrams) of venom remaining in an animal’s body $x$ , days after bitten by snake.

Concept used:

Use data pairs to determine type of function.

Linear function: - The difference of consecutive y-values is constant.

Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

We are given the function:

  

We determine a function which models the data using graphing calculator:

  $a(x)=20.36{(0.5)}^x$

We choose the model using exponential regression.

We determine the amount of venom initially injected into the animal’s body by computing $a(0)$ , the quantity right after being bitten:

  $a(0)=20.36{(0.5)}^0=20.36$ milligrams

Hence,

We choose the model using exponential regression initially injected $20.36$ milligrams into the animal’s body.