Answer :
By solving a system of equations we will see that the function is:
f(x) = 0.55*(1.76)^x
and f(6.5) = 21.88
How to get the exponential equation?
A general exponential function is written as:
f(x) = A*(b)^x
Where A is the initial value and b defines how fast it grows/decays.
In this case we know that:
f(3) = A*(b)^3 = 3
f(8.5) = A*(b)^8.5 = 68
So, we have a system of equations.
To solve this, we can take the quotient between the second and the first equation, so we get:
(A*(b)^8.5)/(A*(b)^3) = 68/3
b^(8.5 - 3) = 68/3
b^(5.5) = 68/3
b = (68/3)^(1/5.5) = 1.76
Now that we know the value of b, we can find the one of A using any of the two equations of the system.
A*(1.76)^3 = 3
A = 3/((1.76)^3) = 0.54
Then the function is:
f(x) = 0.55*(1.76)^x
Evaluating this on x = 6.5 gives:
f(6.5) = 0.55*(1.76)^6.5 = 21.88
If you want to learn more about exponentials, you can read:
https://brainly.com/question/11464095
Answer:
21.86 is the answer in delta
Step-by-step explanation: