Question

Question

The graph of an exponential function has a y-intercept of 10 and contains the point (2, 160). Construct
the function that describes the graph.
Provide your answer below:

Answer 1

f(x) = 10(4^x)

Explanation:

The general form of an exponential function is f(x) = ab^x, where a is the initial value or y-intercept and b is the base raised to the power of x.

We are given that the exponential function has a y-intercept of 10, so we know that a = 10. We are also given that the function passes through the point (2, 160), so we can use this information to find the value of b.

Substituting the values of x and y from the given point into the general equation, we get:

⇒ 160 = 10b^2

Dividing both sides by 10, we get:

⇒ 16 = b^2

Taking the square root of both sides, we get:

⇒ b = ±4

Since b is the base of an exponential function, it must be positive. Therefore, we can choose b = 4.

Substituting the values of a and b into the general equation, we get:

⇒ f(x) = 10(4^x)

Therefore, the exponential function that describes the graph is f(x) = 10(4^x).

Answer 2

Use f(x)=mx + b where f(x)=160 x=2 and b=10 the solve for m

160=m(2) + 10
150 = 2m
75 = m

So the function will be. f(x) = 75x + 10