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Chapter 10: Problem 8

Give the growth factor that corresponds to the given growth rate. \(215 \%\) growth

Short Answer

Expert verified
Answer: The growth factor corresponding to a growth rate of 215% is 3.15.

Step by step solution

01

Convert the percentage to a decimal

To convert the growth rate of 215% to a decimal, divide it by 100. 215 梅 100 = 2.15
02

Add 1

Add 1 to the decimal obtained in Step 1 to find the corresponding growth factor. 1 + 2.15 = 3.15
03

Write the growth factor

The growth factor that corresponds to the given growth rate of 215% is 3.15.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Growth Rate
When we're talking about growth rates, we're discussing how much something increases over time. It's a measure expressed as a percentage.
For example, if you have an initial amount and it becomes larger, the growth rate tells you the rate of that increase relative to the starting amount.
  • A growth rate of 0% means no change.
  • Positive percentages indicate growth, like 215% in our exercise, which means the quantity more than doubled.
  • Negative percentages would indicate a decrease.
Knowing the growth rate is important in many fields, including finance, biology, and economics.
It helps us understand trends and make predictions based on past data.
Percentage to Decimal Conversion
Converting a percentage to a decimal is a fundamental skill in mathematics.
This conversion is essential because decimals allow for easier calculations in many problems.
To convert, follow these simple steps:
  • Take the percentage value, like 215% in this exercise.
  • Divide it by 100. This shifts the decimal point two places to the left.
    For example, 215% becomes 2.15.
Remember that this conversion helps you work with the number in equations and formulas more effectively.
For example, in calculating growth factors.
Mathematical Operations
The main operation required for this task is addition, and it's crucial when finding the growth factor.
After converting the percentage to a decimal, you add 1 to this decimal to find the growth factor.
Here's why this step is necessary:
  • The growth factor represents the total amount after growth, including the original amount.
  • By adding 1 to the decimal, you're essentially accounting for the starting value (which is 1 or 100%).
In our exercise, after converting 215% to 2.15 as a decimal, adding 1 gives us 3.15.
This is the growth factor, showing that the final amount is 3.15 times the initial amount.

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Most popular questions from this chapter

For the functions in the form \(P=a b^{t / T}\) describing population growth. (a) Give the values of the constants \(a, b\), and \(T\). What do these constants tell you about population growth? (b) Give the annual growth rate. \(P=400\left(\frac{2}{3}\right)^{t / 14}\)

Write the exponential functions in the form \(Q=a b^{t}\) and identify the initial value and growth factor. $$ Q=\frac{190}{3^{t}} $$

In Exercises \(7-10\) give the growth factor that corresponds to the given growth rate. \(8.5 \%\) growth

Write a formula for the quantity described. The balance in an interest-bearing bank account, if the balance triples in 20 years.

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