How do you find an exponential function of the form f(x) = ab^x that has the given y-intercept (0, 2); passing through P = (-1, 2/5)?

Solution:

Given,

y-intercept (0, 2) is passing through P = (-1, 2/5)

We know the value of (x, y) in two different cases.

So, we need to find the value of a and b.

2/5 = a × b^-1

2 = a × b⁰

2 = a × 1

a = 2

2/5 = 2 × 1/b

2/5 = 3/b

b = 5

y = 2 × 5^x

Therefore, the equation of the function is y = 2 × 5^x.

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How do you find an exponential function of the form f(x) = ab^x that has the given y-intercept (0, 2); passing through P = (-1, 2/5)?

Summary:

Exponential function of the form f(x) = ab^x that has the given y-intercept (0, 2); passing through P = (-1, 2/5)is y = 2 × 5^x.