Question Video: Determining Whether a Growth Is Exponential or Linear Mathematics

A savings scheme pays interest at a rate of 0.9% per year. Does this represent linear or exponential growth?

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Video Transcript

A savings scheme pays interest at a rate of 0.9 percent per year. Does this represent linear or exponential growth?

Well with an interest rate of 0.9 percent, it’s not a particularly generous saving scheme. But each year, you’ll have 100 percent of what you had last year plus an extra 0.9 percent. So at the end of one year, you’ll have 100.9 percent of the amount that you had at the end of the previous year. Now remember, 100.9 percent means 100.9 divided by 100, which means that, to work out a percentage, we’ve got a multiplier of 1.009. And 1.009 is greater than one, so this is going to be exponential growth.

Let’s just take a look at the formula. First, we need to define some variables. Let 𝑥 equals the year number. Let 𝑦 equals the amount in the savings account, in dollars. And let 𝑎 be the initial amount that we invested in that account, in dollars. So the amount of savings that we’ll have in the account, after year 𝑥, will be our initial amount 𝑎 times 1.009, our multiplier, to the power of 𝑥. And the multiplier is greater than one. And that means we will have exponential growth.

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