Step by step solution to "Model the following data using an exponential function..."

sagnuhh

Answered question

2021-09-29

Model the following data using an exponential function of the form

f (x) = A b^{x}

. Set up a system of equations, and solve it to get A and b.
f(x) is exponential and goes through the points (1, 2) and (4, 6).

toroztatG

Skilled2021-09-30Added 98 answers

Given information:
The required model for the given data is exponential function of the form

f (x) = A b^{x}

.
Find the function f(x) if it goes through (1,2) and (4,6):
The data points are (1,2) and (4,6).
The function f(x) is obtained as given below:

f (x) = A b^{x}

2 = A b^{1} \to (1)

A b = 2

6 = A b^{4}

A b^{4} = 6 \to (2)

\frac{(2)}{(1)} \to \frac{A b^{4}}{A b} = \frac{6}{2} = 3

b^{3} = 3

b = 3^{\frac{1}{3}}

A = \frac{2}{b} = \frac{2}{3^{\frac{1}{3}}}

f (x) = \frac{2}{3^{\frac{1}{3}}} {(3^{\frac{1}{3}})}^{x}

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