Lesson video

Hello, my name is Mr. Clasper, and today we're going to learn how to solve problems using repeated percentage change.

Let's try our first example.

50,000 multiply by 1.

05 to the power of 'a' is equal to 60,775.

3125.

Find the value of 'a'.

Now, the easiest way to solve this problem will be to work systematically.

So, if we calculate 50,000 multiply by 1.

05 that gives us 52,500, which isn't the answer that we wanted.

So 'a' is not equal to one.

If we try the same calculation, multiply by 1.

05 to the power of two, that gives us 55.

125, but we're aiming for 60,775.

3125.

If we carry out the same calculation to the power of three, this gives us 57,881.

25, and if we calculate 50,000 multiplied by 1.

05 to the power of four, we get the answer we wanted.

Therefore the answer, or the solution is that 'a' is equal to four.

Here is a question for you to try.

Pause the video to complete your task and click resume once you're finished.

And here are the solutions.

So remember from the last slide if you work systematically and set up the correct calculation, you can find your answer with relative ease.

So 40,000 multiplied by 1.

03 to the power of three, would give us our answer 43,709.

08, therefore, 'a' must be three.

Likewise for the remaining two calculations, we should get 'b' is equal to five, as 70,000 multiplied by 0.

8 to the power of five, will give us the answer of 22,937.

6.

And we calculate 234, multiply by 0.

63 to the power of two, this will give us our answer of 92.

8746.

Let's have a look at this example.

A bank account contains 30,000 pounds.

This amount increases by 5% every year.

After how many years will there be 34,728 pounds and 75? Well, an increase of 5% would be the same as 105%, and this is equivalent to 1.

05.

Let's find out what happens after one year.

So, after one year, we would have 31,500.

To calculate the amount after two years, we need to multiply by 1.

05 to the power of two, and this would give me 33,075.

If I want to calculate what happens after three years, I need to multiply by 1.

05 to the power of three.

This gives me 34,728 pounds and 75, just like the question should.

So this means that my final answer is three years because I multiply by 1.

05 to the power of three.

Here is a question for you to try.

Pause the video to complete your task, and click resume once you're finished.

And here is the solution.

So to calculate the correct answer, we need to first of all set up the correct calculation.

So, a calculation to set up will be 66,000,000 multiplied by 1.

01 to the power of something, and then we're investigating this until we get 67,999,866, and if you do this correctly, you should find that 66,000,000 multiplied by 1.

01 to the power of three will help you achieve this answer.

Therefore, the correct final answer was three years.

Let's take a look at this example.

A town has a population of 4,000.

The population increases by 6% every year.

After how many years will the population increase by more than 600? So setting up our calculation, if I multiply by 1.

06, this will be equivalent to finding 106% or increasing by 6%.

So 4,000 multiplied by 1.

06 would give me 4,240.

This is an increase of 240, which is not more than 600.

So, I'm going to keep going.

If I calculate 4,000 multiplied by 1.

06 to the power of two, this gives me 4,494.

4, which will be an increase from the original population of 494.

4.

This still isn't greater than 600, so I'm going to keep going 4,000 multiply by 1.

06 to the power of three, would give me 4,764.

064, and this will be an increase of 764.

064.

This means that it's after three years that the increase would be more than 600.

Here are some questions for you to try.

Pause the video to complete your task, and click resume once you're finished.

And here are your two solutions.

So, for the first calculation, it's after two years that Alan makes a profit of more than 500 pounds.

So, if we calculate 5000 multiplied by 1.

05 to the power of two, this gives us a figure which is greater than 5,500, which will be our profit of 500.

And for question number four, if we make a calculation of 4,000, multiplied by 0.

89 to the power of six, this would give us a value which is less than 2,000 or less than 4,000, which is our original amount, so, therefore, the correct answer was six years.

Here is your last question.

Pause the video to complete your task, and click resume once you're finished.

And here is your final solution.

So, a good strategy for this question is to compare what would happen to Math students across a given number of years compared with English students across a given number of years.

If we do this correctly, you should find that after three years, there will be approximately 27.

375 Math students, and after three years, there would approximately be 26.

62 English students, therefore, it's after three years, there will be more Math students than English students.

And this brings us nicely to the end of our lesson.

So, today you've learned how to solve problems with repeated percentage change.

Why not put your new skills into practise and try our exit quiz and boost your confidence further.

Hopefully I'll see you soon.