Question

An exponential function f(x) = ab passes through the points (0, 7000) and (3, 7). What are the values ofa and b?a=b=

Answer 1

Answer:

a = 7000

b = 1/10

Explanation:

An exponential function is of the form:

$f(x)=ab^x$

The given points:

(0, 7000) and (3, 7)

Form two equations and solve for a and b

$\begin{gathered} f(x_1)=ab^{x_1}...........(1) \\ \\ f(x_2)=ab^{x_2}.............(2) \end{gathered}$

Substitute x₁ = 0, f(x₁) = 7000, x₂ = 3, f(x₂) = 7 into the two equations

$\begin{gathered} 7000=ab^0 \\ \\ 7000=a(1) \\ \\ a=7000 \end{gathered}$

Substitute x₂ = 3, f(x₂) = 7, and a = 7000 into equation (2)

$\begin{gathered} 7=7000b^3 \\ \\ \frac{7}{7000}=b^3 \\ \\ \frac{1}{1000}=b^3 \\ \\ b=\sqrt[3]{\frac{1}{1000}} \\ \\ b=\frac{1}{10} \end{gathered}$

a = 7000

b = 1/10