171k views
1 vote
An exponential function f(x) = ab passes through the points (0, 7000) and (3, 7). What are the values ofa and b?a=b=

1 Answer

4 votes
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

User Avikrit Khati
by
8.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories