Write an exponential function in the form y = ab^x that goes through points (0,20) and (2,320).

The exponential function is given by y = 20(3.4)ˣ

An exponential equation is in the form:

y = abˣ

Where y, x are variables, b is the factor and a is the initial value of y.

Given the points (0,20) and (2,320):

At point (0, 20):

20 = ab⁰

a = 20

At point (2, 230):

230 = 20(b)²

b² = 11.5

b = 3.4

The exponential function is given by y = 20(3.4)ˣ

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y = 20*4^x

Step-by-step explanation:

to find the value of the constants a and b, we just need to use the points given in the equation and solve the system of equations:

point (0,20): x = 0 and y = 20:

20 = a*b^0 = a*1 = a

a = 20

point (2,320): x = 2 and y = 320

320 = 20 * b^2

b^2 = 16

|b| = 4

b = 4 or b = -4

So we have two exponencial equations that pass through these points:

y = 20*4^x and y = 20*(-4)^x

As the questions asks for just one equation, we can answer y = 20*4^x

step-by-step explanation:

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