Answer:
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
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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