Video: Pack 3 • Paper 2 • Question 8

Pack 3 • Paper 2 • Question 8

04:49

Video Transcript

A city’s council decided to increase its number of trees by 6.5 percent each year in the next two years. In January 2018, the number of trees was 142000. What will be the tree population in January 2020 according to this plan? Give your answer correct to three significant figures.

We’re told in the question that the city council hope to increase the number of trees by 6.5 percent each year. This means that, assuming they don’t cut down any of their trees, each year, they will have 100 percent of the trees they started with plus an additional 6.5 percent. So they’ll have 106.5 percent of the number of trees they started with.

We need to work out what 106.5 percent of 142000 is in order to find the number of trees in 2019. To do this, we need to convert our percentage of 106.5 percent to a decimal that we can then use as a multiplier.

To convert from a percentage to a decimal, we divide by 100, giving 1.065. 142000 multiplied by 1.065 is 151230. So this is the number of trees the council hope to have in 2019. We then multiply by 1.065 again to find the number of trees the council hope to have in 2020, giving 161059.95.

The question asks us to give our answer correct to three significant figures. So we need to round this value. The first significant figure is the first nonzero digit in the number, so that’s one. The second significant figure is the next digit, six. And the third significant figure is the next digit, one. Looking at the fourth significant figure, it’s a zero, which tells us that we can round down. The tree population in 2020, assuming everything goes to plan, will therefore be 161000, correct to three significant figures.

The aim of the council is to have as many trees as inhabitants in the city in five years. There are 220000 inhabitants in this city. Work out in which year the city will have over 220000 trees if the tree population increases at a rate of 6.5 percent each year.

We’ve already worked out that if the tree population increases at a rate of 6.5 percent each year, then the tree population in 2020 will be 161000, correct to three significant figures. To work out in which year the tree population will exceed 220000, we just need to keep multiplying by this decimal of 1.065. This gives 171465, so we need to keep going.

A quick way to do this on your calculator is to type in the starting value, 161000, press enter, and then type multiplied by 1.065. You can then keep pressing enter, and your calculator will keep multiplying the previous value by 1.065.

In 2022, the tree population will be 182610. Now this value does actually have a decimal. But I’ve just written it down to the nearest integer as we need to keep going anyway as the tree population hasn’t yet exceeded 220000.

If I keep multiplying by 1.065 and recording the values in each of the subsequent years, I can see that the first year at which the tree population exceeds 220000 is 2025. So our answer to this part of the question is 2025, which means that if the tree population increases at a rate of 6.5 percent each year, the council won’t achieve their aim, as this is more than five years after 2018.

The final part of the question asked us what should the council decide if they want to reach a tree population of 220000 trees by 2023. So what should they do if they do want to achieve their aim of having as many trees as inhabitants within the next five years? Well, we’ve seen the increase in the number of trees by 6.5 percent each year won’t get them to their aim fast enough. So if they want to achieve their aim, they need to increase the rate at which the tree population increases to a value beyond 6.5 percent each year.

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