Solving Exponential Equations II

LG: I can use trial and error to solve exponential equations

Using your Calculator to Solve Exponentials Equations

• Rational exponents can be calculated on a calculator using the button

• Example: To find the 7th root of 983, you would type:

• How could you do the same calculation without using ?

Recall: Solving for a base using inverse operations

x3 = 216 x1/3 = -3

4x2 = 100 3x2 + 2 = 149

Practice:x4 = 81 17x1/4 = 209 2x3 – 9 = -

25

Recall: Solving for an exponent by finding a common base

2x = 29 23x-3 = 29 3x = 9x+2

Practice:32x -7 = 3-x

4x+24 = 643x

Minds On…

• Solve for x:

9x+2 = 272x

Solving exponential equations using trial and error

3x = 5 7x = 612x =

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1

6

Application• A lab technician can model the growth of bacteria

using the equation P = 72(2)x, where P is the total population after x hours

• There are currently 72 cells in the population. Use the equation to estimate when there will be 648 cells

Application

• The formula for Compound Interest is: A = P(1+i)n

• $25000 was invested for 3 years in an account that pays interest compounded annually. If the investment was worth $28500 after three years, what was the interest rate?

Homework

• Complete ‘Solving Exponential Equations’ Handout