Question

Find a formula for the exponential function passing through the points.

a) f(x) = e^(2x)
b) f(x) = e^(-2x)
c) f(x) = 2ˣ
d) f(x) = e^(x²)

Answer 1

To find a formula for an exponential function passing through the given points, we need to determine the initial value and base of the exponential function for each equation.

Step-by-step explanation:

To find a formula for an exponential function passing through the points, we need to use the general form of the exponential function: y = ab^x, where a is the initial value and b is the base of the exponential function.

a) For f(x) = e^(2x), the initial value is e^0 = 1 and the base is e. So the formula is f(x) = e^x.

b) For f(x) = e^(-2x), the initial value is e^0 = 1 and the base is e^(-2). So the formula is f(x) = (e^(-2))^x.

c) For f(x) = 2^x, the initial value is 2^0 = 1 and the base is 2. So the formula is f(x) = 2^x.

d) For f(x) = e^(x^2), the initial value is e^(0^2) = e^0 = 1 and the base is e^(x^2). So the formula is f(x) = (e^(x^2))^x.