3.3 Percent Change
Marilyn Nielson
Applications
In general, we are looking for change when we monitor phenomena in the field. This change is often best understood if expressed as a percent. For example, in 2018 out of 245 plots sampled, five included the rare plant skinny moonwort (Botrychium lineare). This year we hit all of the original plots and found eighteen with skinny moonwort. By what percent has the occurrence of this species changed?
Let’s keep our momentum using proportions to solve percent problems! Percent change problems are a little different, because we need to add or subtract a percent to arrive at our final answer.
[latex]\frac{Final (\text{or current number})}{Starting\text{(or base number)}} = \frac{100\pm percent change}{100}[/latex]
The “Final” number is the number you have after the percent change has been applied. The “Starting” number can also be called the “Base”. It’s the number you begin with before the percent change has been applied. This number will generally be earlier in time and represents the before condition. When you are dealing with increase, growth, birth, you’ll add the percent of that change to 100. When you are dealing with mortality rates, loss, or decrease, you’ll subtract that percent change from 100.
When you’re finding a quick percent that something changed by. It may be easiest to take the difference between the two numbers and divide that difference by the starting number. This will give you a decimal and to get the percent multiply by 100 and add the % sign.
[latex]\frac{Final-Starting}{Staring}\cdot 100 =\text{Percent change}[/latex]
Examples: Beginning Percent Change
A) What do you end up with when you increase 140 by 10%?
B) What do you end up with when you decrease 140 by 10%?
C) If you start with 110 and end with 76, what is the percent change?
D) If you start with 65 and end up with 123, what is the percent change?
E) If you end with 650 after losing 12%, what did you start with?
F) If you end with 1,200 after gaining 3%, what did you start with?
View the answers.
Watch the solutions video.
Examples: Applied Percent Change
A) Tax is 9.2% in Spokane County. Your organization wants to purchase a $620,000 parcel of 20 acres. How much will it cost after tax?
B) As a wildland firefighter, you get 20% off a purchase of White’s boots. If the boots cost $699, how much will you pay?
C) This year 1,200 people visit Antelope Wildlife Refuge. Next year, 1,450 people visit. Visitorship has changed by what percent?
D) Temperatures in Lake Michigan are expected to rise by 3% over the next five years. If temperatures currently average 75.468ºF – what will they be in five years?
E) An unexpected freeze leaves you with 112 of the 148 saplings you planted. What percent change is this?
F) You expect 50% loss of trees planted on a mitigation site. If you need to end the season with 2,500 trees, how many should you plant at the beginning of the season?
G) You’re packing fertilizer stakes for shipment. Five percent of stakes will break during shipment. If you need 1,200 unbroken stakes to arrive at the greenhouse – how many should you pack?
View the answers.
Watch the solutions video.
Problem Set 3.3
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I am buying supplies to build funnel traps to catch small mammals. I need 50 feet of wire mesh. Wire mesh costs $2.15 per linear foot. Sales tax is 8.7%. How much money do I need to include in the budget for wire mesh?
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The elk herd on Tekoa Mountain is growing by 15% per year. If there were 14 elk on the mountain last year, how many will be on Tekoa Mountain this year? Assuming the growth rate stays constant, how many elk will be on the mountain next year?
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The elk herd on Tekoa Mountain is growing by 15% per year. If there were 14 elk on the mountain last year, how many will be on Tekoa Mountain this year?
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Average spring runoff on the St. Joe River is 1,200 cfs. Runoff is expected to be 10% higher this year due to an especially snowy winter. What will runoff be this year?
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Drilling costs are increasing by 7% per year. This year an 800 foot well cost $2,500 to drill. How much will it cost to drill the same well next year?
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I counted 45 sage grouse on the sand hill lek this year. If the population is growing by 2% per year, how many sage grouse were on the lek last year?
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I just found a 20% off coupon for any single item at the local hardware store. I need to buy a post hole digger to prepare holes for pitfall traps. The post hole digger normally costs $35. How much will it cost after I use my coupon? (excluding tax)
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18% of newly planted cottonwoods won’t survive their first winter. To meet the requirements of my permit, I need to have 375 cottonwoods alive on my mitigation site next summer. How many cottonwoods do I need to plant this fall?
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Visits to Itasca State Park are down by 5% this year. If 1,234 people visited the park last year, how many visited the park this year?
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An average bull elk loses 16% of his body weight during the rut. If a bull elk goes into the winter weighing 980 lbs, what was his weight before the rut?
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We lose 18% of bats in each colony to white-nose syndrome. If I find 88 dead bats, how many total bats were in the colony?
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Last year 1,234 people visited Itasca State park. This year 1,300 visitors registered at the park. Park attendance is increasing by what percentage?
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I planted 250 willows on my mitigation site this summer. I counted the willows in October and found 178. What percent mortality are my willows experiencing?
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A population of voles can increase at 4% per year. Last year we estimated the population at 135 voles. How large might the population be this year?
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A stand of ponderosa pine grows 3% per year. If I had 1,500 board feet of timber in my stand last year, how many board feet are present this year?
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I want to know how large the wolf population in central Idaho was in 1949. In 1950, the population was estimated at 58. If I know the population grew at 1.3%, how many wolves were present in 1949?
