Find the formula for an exponential function that passes through 2 points given:
(x,y)=(2,2.7) and (x,y)=(5,72.9)
f(x)=
To find the formula for an exponential function that passes through two points, we can use the general form of an exponential function:
y = a * b^x
where a is the initial value and b is the growth factor.
Using the two given points, we can set up a system of equations:
2.7 = a * b^2
72.9 = a * b^5
Dividing the second equation by the first equation, we get:
(72.9/2.7) = b^3
Taking the cube root of both sides, we get:
b = 6
Substituting this value of b into either of the original equations, we can solve for a:
2.7 = a * 6^(-2)
a = 2.7 * 6^2
Therefore, the formula for the exponential function that passes through the two given points is:
f(x) = 2.7 * 6^(x-2)
AAAaannndd the bot gets it wrong yet again!
(72.9/2.7) = b^3
Taking the cube root of both sides, we get:
b = 3
2.7 = a * 3^(2)
a = 3/10
f(x) = (3/10)*3^x