Question Video: Creating Exponential Equations in Two Variables Mathematics

The number of people visiting a museum is decreasing by 3% 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.

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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.

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