Find the exponential function f(x)=ca^x given two points (1,6) (3,24)

[tex]f(x)=ca^x\to y=ca^x\\\\(1;\ 6)\to x=1;\ y=6\\(3;\ 24)\to x=3;\ y=24\\\\\text{substitute the values of x and y to the equation:}[/tex]

[tex]\left\{\begin{array}{ccc}6=ca^1&\to c=\dfrac{6}{a}\\24=ca^3\end{array}\right\\\\substitute\\\\24=\dfrac{6}{a}\cdot a^3\\\\24=6a^2\ \ \ |:6\\\\a^2=4\to a=\sqrt4\to a=2\\\\substitute\\\\c=\dfrac{6}{2}=3[/tex]

[tex]Answer:\ \boxed{f(x)=3\cdot2^x}[/tex]

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-08-02T11:56:22+02:00

The exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have:

An exponential function:

f(x) = c(a)×

The two points are given:

(1,6) and (3,24)

Plug x = 1

f(x) = 6

6 = c(a) ...(I)

Plug x = 3

f(x) = 24

24 = c(a)³ ...(II)

Divide equations (1) and (II)

24/6 = c(a)³/c(a)

4 = a²

a = 2

Plug a = 2 in equation I

6 = c(2)

c = 6/2

c = 3

The exponential function:

f(x) = 3(2)×

Thus, the exponential function is f(x) = 3(2)× which is passes throgh the two points (1,6) and (3,24).

Learn more about the exponential function here:

brainly.com/question/11487261

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