Warm upIn 1991 the population of Humpback whales was 5263. The Humpback population decreases at an annual rate of 1.5%.

What is the exponential equation modeling this decay?

What will the Humpback population be in 2012?

Warm up Answer

• Equation:

• Number of whales in 2012:

y= 3831 whales

𝑦=5263 (1− .015 )𝑥

Rational Exponents and Roots

Remember:

• What is the difference between a Power function and an Exponential function?

• Power has variable in the base and exponential has variable in the exponent.

• (you need to know this for #1 on the homework)

Definition of Rational Exponents

So….

• OR • Also remember So, reciprocals of fractions cancel each other out.

Example 1

Solution

• Rewrite with a fraction• =47 Set equal to original value• Raise both sides to the power of

the reciprocal to cancel out the exponent• Put in the calculator to simplify.

Example 2: You try!

Answer:

352.33

Example 3: what if there is a coefficient?

3√ 4 𝑥2+8.5=19.8

Answer

• Original• Subtract 8.5• Change cube-root to a fraction• Cube both sides to cancel • Divide by 4• Raise both sides to the

Remember from way back when…

• The general equation for transformation of functions…

Example 4• The original equation in black is . Write an

equation for the shifted function in red.

Answer

𝑓 (𝑥 )=(−𝑥−5 )34+1

Homework

• 5.3 Worksheet• 1 all• 2 a-c• 3 a-f• 4 a-c