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How are exponential functions used in real life?

How are exponential functions used in real life?

Exponential functions are often used to represent real-world applications, such as bacterial growth/decay, population growth/decline, and compound interest. Suppose you are studying the effects of an antibiotic on a certain bacteria. Every 15 minutes, you check the petri dish and count the number of bacteria present.

What is a real life example of exponential growth?

One of the best examples of exponential growth is observed in bacteria. It takes bacteria roughly an hour to reproduce through prokaryotic fission. If we placed 100 bacteria in an environment and recorded the population size each hour, we would observe exponential growth.

How are logarithms used to solve exponential functions?

How To: Given an exponential equation in which a common base cannot be found, solve for the unknown. Apply the logarithm of both sides of the equation. If one of the terms in the equation has base 10, use the common logarithm. If none of the terms in the equation has base 10, use the natural logarithm.

How do you do rationals?

  1. Step 1: Factor the numerator and the denominator.
  2. Step 2: List restricted values.
  3. Step 3: Cancel common factors.
  4. Step 4: Simplify and note any restricted values not implied by the expression.

How do you simplify expressions with rational exponents?

Subtract the “x” exponents and the “y” exponents vertically. Then add the exponents horizontally if they have the same base (subtract the “x” and subtract the “y” ones). Finally move the negative exponent to the denominator.

When will I use exponents in real life?

Another example of using exponents in real life is when you calculate the area of any square. If you say “My room is twelve foot by twelve foot square”, you’re meaning your room is 12 feet × 12 feet — 12 feet multiplied by itself — which can be written as (12 ft)2. And that simplifies to 144 square feet.

How do you simplify radicals examples?

Simplify the expressions both inside and outside the radical by multiplying. Simplify by multiplication of all variables both inside and outside the radical….Simplify the following radical expressions:

  1. 2 + 9 –√15−2.
  2. 3 x 4 + √169.
  3. √25 x √16 + √36.
  4. √81 x 12 + 12.
  5. √36 + √47 – √16.
  6. 6 + √36 + 25−2.
  7. 4(5) + √9 − 2.
  8. 15 + √16 + 5.

How do you solve a radical step by step?

Step 1: Find the prime factorization of the number inside the radical. Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical.

What are the rules for simplifying radicals?

NOTE: A simplified radical contains no fractions and no radicals in the denominator. If the denominator is a one-termed radical expression, multiply the numerator and the denominator by a radical that will make the radicand of the denominator a perfect-n.

What are the law of radicals?

LAWS OF RADICALS. Definition: A radical represents a fractional exponent in which the numerator of the fractional exponent is the power of the base and the denominator of the fractional exponent is the index of the radical.

What is the rule for multiplying radicals?

Basic Rule on How to Multiply Radical Expressions. A radicand is a term inside the square root. We multiply radicals by multiplying their radicands together while keeping their product under the same radical symbol.

What happens when you add radicals?

To add or subtract radicals, the indices and what is inside the radical (called the radicand) must be exactly the same. If the indices and radicands are the same, then add or subtract the terms in front of each like radical. If the indices or radicands are not the same, then you can not add or subtract the radicals.

Can I add two radicals?

Step 2: Combine like radicals. You can only add or subtract radicals together if they are like radicals.