Exponential function f(x) passes through the points (3,6) and (7,18) determine the value of F(20)To the nearest integer

An exponential function can represent growth or decay.

The value of f(20) is 673

An exponential function is represented as:

At point (3,6), we have:

At point (7,18), we have:

Divide both equations

Take 4th roots of both sides

Rewrite as:

Substitute 1.32 for b in

Divide both sides by 2.3

So, the function is:

When x = 20, we have:

Rewrite as:

Hence, the value of f(20) is 673

Read more about exponential functions at:

link

A generic exponential function can be written as:

f(x) = A*e^(b*x)

Where A and b are real numbers, that we need to find.

We know that the points (3, 6) and (7, 18) are solutions to the equation, then we have that:

A*e^(b*3) = 6

A*e^(b*7) = 18

This is a system of equations, to solve this we can take the quotient between the two equations, so we remove the variable A.

(A*e^(b*7))/(A*e^(b*3)) = 18/6

e^(b*7)/e^(b*3) = 3

e^(b*7 - b*3) = 3

e^(4*b) = 3

Now we can apply the Ln(x) to both sides, because:

Ln(e^y) = y

then:

Ln(e^(4*b)) = Ln(3)

4*b = Ln(3)

b = Ln(3)/4

Then we have:

f(x) = A*e^(Ln(3)/4*x)

And we can use one of the equations to find the value of A. for example:

6 = A*e^(Ln(3)/4*3)

6/e^(Ln(3)/4*3) = 2.632

Then the exponential function is:

f(x) = 2.632*e^(Ln(3)/4*x)

Then we have that:

f(20) = 2.632*e^(Ln(3)/4*20) = 639.576

Rounding to the next integer, we have:

f(20) = 640

b

step-by-step explanation:

if a was wrong then it has to be b it cant be c either because not all the y intercepts are the same!

ok now , i would like brainlest plz

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?