Writing and interpreting exponential functions

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y = 6(0.14)^x

• y = 6(1 + 14)^x

• y = 6(1.14)^x

• y = 6(0.86)^x

Which is an exponential decay equation that is shifted 1 units right and 3 units down?

• 
• 
• 
• 

Sim City currently has 100,000 people and the population is decreasing 5.6%.

Which equations represent this scenario? Select all that apply.

• $y=100,000\left(1-5.6\right)^x$

• $y=100,000\left(1-0.56\right)^x$

• $y=100,000\left(1-0.056\right)^x$

• $y=100,000\left(0.944\right)^x$

• $f\left(t\right)=100,000\left(0.944\right)^t$

Write the equation for the following situation:
You buy a car for $26,500.  The car depreciates in value by 20% a year.  

• A = 26500(1+0.2)^t

  A = 26500(1.2)^t

• A = 26500(1+0.8)^t

  A = 26500(1.8)^t

• A = 26500(1-0.2)^t

  A = 26500(0.8)^t

• A = 26500(1-0.02)^t

  A = 26500(0.98)^t

Warren invested $50,000 into an off-shore savings account with an astounding annual interest rate of 6%. Write an equation to model the account balance over time, x, in years.

• y = 50000(1.06)^x

• y = 50000(6)^x

• y = 6(50000)^x

• y = 1.06(50000)^x

Which of the following equations shows an initial value of 21 and is an exponential growth?

The population of a city is growing at the rate of 0.4% per year. In 2007 it was 83,000 people. Which function represents the towns population “t” years after 2007?

• 
• 
• 
• 

In the year 1900, the total number of metric tons of copper produced in the world was 495,000. Each year since 1900, the total number of metric tons of copper produced has increased on average by 3.25% over the amount produced the previous year.

Which function models the total number of metric tons of copper produced in the year that is x years since 1900?

A laser beam with an output of 6 milliwatts is focused at a series of mirrors. The laser

beam loses 2% of its power every time it reflects off of a mirror. The power p (n) is an

exponential function of the number of reflections in the form of p (n) = ab n . Write the

equation p (n) for this laser beam. Determined the values of a and b. Copy and replace the letter with the right number or letter. LEAVE the spacing it will mark it wrong and it will stay WRONG.

p (n) = a (b) ^ x

Write the rule for the sequence below:

5, 15, 45, 135, . . .

• t(n) = 5(3)

• t(n) = 3(5)

• t(n) = 5(3)ⁿ

• t(n) = 3(5)ⁿ