200k views
1 vote
0.

DETAILS
Model the data using an exponential function f(x) = Ab".
X
0
1
2
f(x)
400
240
144
f(x) =
Need Help?
Read It

0. DETAILS Model the data using an exponential function f(x) = Ab". X 0 1 2 f-example-1
User Eyevan
by
8.5k points

2 Answers

4 votes
I think The answer is 250
User Tim Wachter
by
8.3k points
6 votes

The data is modeled by the exponential function f(x) = 400(0.6)^x, where 400 represents the initial amount and 0.6 represents the decay factor for each time interval.

Step-by-step explanation:

Modeling data with an exponential function involves writing a function of the form f(x) = Abx, where A is the initial amount, b is the base of the exponential and represents the growth factor, and x is the exponent representing time or number of intervals.

Given the data points f(x)=400 when x=0, f(x)=240 when x=1, and f(x)=144 when x=2, we can observe that each time x increases by 1, the function decreases to 60% of its previous value, suggesting a decay factor of 0.6. Therefore, our base b is 0.6.

We can calculate the value of A by using the initial condition, where x is 0. Since 400 = Ab0, and b0 is 1, it follows that A = 400.

The exponential function representing this data set is therefore: f(x) = 400(0.6)x.

User Hillery
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories