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

Step-by-step 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 \\ \\ (7)/(7000)=b^3 \\ \\ (1)/(1000)=b^3 \\ \\ b=\sqrt[3]{(1)/(1000)} \\ \\ b=(1)/(10) \end{gathered}`

a = 7000

b = 1/10