Answer :

The formula for f(x) an exponential function is f(x) =1760(2.71828)^(0.01732x).

Let f(x) be an exponential function such that f(-1) = 220 and f(40) = 704.

The exponential function is of the form

f(x) = abx,

where a is the initial value, b is the base, and x is the exponent. We can use these values to solve for a and b.

Let's first solve for b. We have:

f(40) = ab

40 = 704

Dividing both sides by 220, we get:

f(40) / f(-1) = (ab40) / (ab-1)

= 704 / 220

Simplifying the left side, we get:

b41 = 704 / 220

= 8

Dividing both sides by b, we get:

b40 = 8 / b

Now, we can substitute this into our equation for f(40):

f(40) = ab

40 = a(8 / b)

= 8a / b

Next, we can solve for a using the value of f(-1):

f(-1) = ab-1 = 220

Substituting in b40 = 8 / b, we get:

ab-1 = 220

a(8 / b)-1 = 220

a(b / 8) = 220

Multiplying both sides by 8/b, we get:

ab = 220(8/b)

= 1760/b

Now, we can substitute both of these values into our equation for f(x):

f(x) = ab

x = (1760/b)

(bx) = 1760(x / 40)

So the formula for f(x) is

f(x) = 1760(2.71828)^(0.01732x).

To know more about equation visit;

https://brainly.com/question/29657983

#SPJ11

Thank you for reading the article Find a formula for f x an exponential function such that f 1 220 and f 40 704. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions