Question

The graph represents the number y of visitors to a new art gallery after x months. Write an exponential function that represents this situation. Approximate the number of visitors, to the nearest person, after 5 months.

Y=____

About ___ visitors

Answer 1

• y = 40(1.5)ˣ
• About 304 visitors

Explanation:

Formula for exponential function:

• y = abˣ

Use two points from the graph to determine the function:

• (0, 40) and (1, 60)

Substitute the coordinates and work out the values of a and b:

• 40 = ab⁰ ⇒ 40 = a
• 60 = ab¹ ⇒ 60 = ab ⇒ 60 = 40b ⇒ b = 60/40 ⇒ b = 1.5

The function is:

• y = 40(1.5)ˣ

The number of visitors after 5 months:

• y = 40(1.5)⁵ = 304 (rounded up)