warm up in 1991 the population of humpback whales was 5263. the humpback population decreases at an...

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