Depending upon your grade or school level, terminology may differ. So this is a question that can cross over from middle school math to college or university math. And it's something that could be from a finance course too. So we don't know what grade level you're in or the class itself. But I will do my best to keep things simpler.
There is a formula: 𝐀 = 𝐏 (𝟏+𝐫)ᵗ
𝐀 is the amount you'll have in the end. And 𝐏 is the amount you began with. 𝐫 is the annual rate and 𝐭 is the number of years. The annual multiplier would be (𝟏+𝐫). So the fist thing you need to do is solve for the rate.
$5,750 = $16,000 multiplied by (1+r) to the fifth power. Dividing both sides by $16,000 would give you 0.359375 = (𝟏+𝐫)⁵.
The next step would be to take the fifth root of both sides. That would leave you with 0.81490986 = 𝟏+𝐫. Subtracting 1 from both sides will give you the your rate, which comes out to 0.18509014. This is the rate as a decimal and would represent the annual loss of value in each of those five years. To make this a percentage, you'd multiply by 100. And then round your answer to however many decimal places your teacher wants.
Your multiplier would be taking that 0.18509014 and adding 1 to it. Then rounding your answer to however many decimal places your teacher wants.
divide the end value by the beginning value. take natural log of result. divide by number of years. do exponentiation of that result. answer is the annual percent decline in value, compounded one a year.
Answers & Comments
Depending upon your grade or school level, terminology may differ. So this is a question that can cross over from middle school math to college or university math. And it's something that could be from a finance course too. So we don't know what grade level you're in or the class itself. But I will do my best to keep things simpler.
There is a formula: 𝐀 = 𝐏 (𝟏+𝐫)ᵗ
𝐀 is the amount you'll have in the end. And 𝐏 is the amount you began with. 𝐫 is the annual rate and 𝐭 is the number of years. The annual multiplier would be (𝟏+𝐫). So the fist thing you need to do is solve for the rate.
$5,750 = $16,000 multiplied by (1+r) to the fifth power. Dividing both sides by $16,000 would give you 0.359375 = (𝟏+𝐫)⁵.
The next step would be to take the fifth root of both sides. That would leave you with 0.81490986 = 𝟏+𝐫. Subtracting 1 from both sides will give you the your rate, which comes out to 0.18509014. This is the rate as a decimal and would represent the annual loss of value in each of those five years. To make this a percentage, you'd multiply by 100. And then round your answer to however many decimal places your teacher wants.
Your multiplier would be taking that 0.18509014 and adding 1 to it. Then rounding your answer to however many decimal places your teacher wants.
For annual you could use A = P (1 - r)^t
5750 = 16000 (1 - r)^5
5750/16000 = 0.359375 = (1 - r) ^ 5
fifth root (0.359375) = 1 - r = approx. 0.8149
so r = 1 - 0.8149 = 0.1851 = 18.51%
divide the end value by the beginning value. take natural log of result. divide by number of years. do exponentiation of that result. answer is the annual percent decline in value, compounded one a year.