Video Transcript
The number of people visiting a
museum is decreasing by three percent a year. This year there were 50,000
visitors. Assuming the decline continues,
write an equation that can be used to find 𝑉, the number of visitors there will be
in 𝑡 years’ time.
When we’re dealing with the percent
decrease, we’re not dealing with a linear function, so we know we’ll need an
exponential function to model this. This means we’ll use the general
form 𝑓 of 𝑥 equals 𝐴 times 𝑏 to the 𝑥 power. Our 𝑏-variable is the rate of
change. The 𝑥-variable represents the unit
of time we’re measuring. And 𝐴 represents the initial
value. We need to be clear here that we
want to model the number of visitors there will be at the museum.
A decrease in three percent of the
visitors means that 97 percent of the visitors are maintained. Since we’re modeling the number of
visitors, we’ll use 97 percent. We’ll write this percent in decimal
form 0.97. We know that our 𝑥-value is being
measured in 𝑡 years. And our starting value, our initial
value, are the 50,000 visitors from this year. Our equation is modeled with a
capital 𝑉 so that we have the equation 𝑉 equals 50,000 times 0.97 to the 𝑡
power.
