03-02 Exponential Models

Find the equation of an exponential function that passes through the points (0, 4) and (3, 0.5).

• $y=4\left(0.5\right)^x$

• $y=3\left(0.5\right)^x$

• $y=4\left(-\frac{7}{6}\right)^x$

• $y=-\frac{7}{6}\left(4\right)^x$

Find an exponential model for the given table of values.

• $y=10\left(2\right)^x$

• $y=2\left(10\right)^x$

• $y=5\left(2\right)^x$

• $y=10\left(\frac{1}{2}\right)^x$

The population of a village is currently 175,000 but is decreasing by 2.5% annually.  Approximate the population in 25 years?

• 92929

• 1.5543

• 324440

• 189665

A sample of 2500 grams of a certain substances decays so that after 10 days, only 1500 grams remain. How much of the sample will remain after 53 days?

• 167

• 19912

• 7800

• 2800

Assuming carbon-14 has a half-life of 5730 years and a wooden spear originally has 10,500 atoms of carbon-14, what is the concentration of carbon-14 after 7000 years?

• 4502

• 24487

• 18518

• 5954

The population of the Emerald City was 16,000 in 2000. The average annual growth rate is 1.25%. What is the population of the Emerald City in 2019?

• 20259

• 12599

• 149975

• 1266

The doubling time of a certain germ is 6.7 hours. If there are 150,000 germs initially, how many germs will be present after 1 hour?

• 166349

• 300000

• 15595246

• 144

If $5000 is invested in an account that increases by 4% annually, how much will be in the account after 10 years?

• 7401.22

• 144627.33

• 52000.00

• 33241.63

Find the equation of an exponential function that passes through the points (0, 2) and (4, 512).

•  $y=2\left(4\right)^x$ 

•  $y=4\left(2\right)^x$ 

•  $y=2\left(\frac{1}{4}\right)^x$ 

•  $y=\frac{1}{4}\left(2\right)^x$ 

Find the equation of an exponential function that passes through the points  $\left(2,\ -\frac{3}{32}\right)$ and  $\left(5,\ -\frac{3}{2048}\right)$ .

•  $y=-\frac{3}{2}\left(\frac{1}{4}\right)^x$ 

•  $y=-\frac{1}{4}\left(\frac{3}{2}\right)^x$ 

•  $y=\frac{3}{2}\left(-\frac{1}{4}\right)^x$ 

•  $y=\frac{1}{4}\left(-\frac{3}{2}\right)^x$