Find the equation of exponential function, has points (1,4) y_ intercept is 2 ?

To find the equation of an exponential function given the points (1,4) and a y-intercept of 2, we can use the general form of an exponential function:

y = a * b^x

where "a" is the y-intercept and "b" is the base of the exponential function.

Given that the y-intercept is 2, we have:

2 = a * b^0
2 = a * 1
a = 2

Now, we can use the point (1,4) to find the value of "b":

4 = 2 * b^1
4 = 2b
b = 2

Therefore, the equation of the exponential function is:

y = 2 * 2^x

or

y = 2 * (2^x)

The equation of an exponential function is:

$$ y = a \cdot b^x + c $$

where a is the initial value (y-intercept), b is the base, c is the vertical shift, and x is the independent variable.

Given that the y-intercept is 2, we can substitute a = 2 into the equation and get:

$$ y = 2 \cdot b^x + c $$

Now, we can use the given point (1,4) to find the values of b and c. Substituting x = 1 and y = 4 into the equation, we get:

$$ 4 = 2 \cdot b^1 + c $$
$$ 4 = 2b + c $$

We also know that when x = 0, y = 2, so we can use this to find the value of c. Substituting x = 0 and y = 2 into the equation, we get:

$$ 2 = 2 \cdot b^0 + c $$
$$ 2 = 2 + c $$
$$ c = 0 $$

Substituting c = 0 into the first equation, we get:

$$ 4 = 2b $$
$$ b = 2 $$

Therefore, the equation of the exponential function is:

$$ y = 2 \cdot 2^x $$
$$ y = 2^x + 2 $$