Exponential Models

The population of Winnemucca, Nevada, can be modeled by  $P=6191(1.04)^t$  where t is the number of years since 1990. What was the population in 1990? (t = 0)

• 0

• 104

• 6191

• 6438

A population of fish can be modeled by the function  $P=8000(0.94)^t$ , where t is in years. What is the population of fish after 10 years?

• 14327

• 4308

• 839

• 7680

The amount of ants in a colony, f, that is decaying can be modeled by $f(x)=800(.87)^x$ , where x is the number of days since the decay started.
Suppose  $f\left(20\right)=49$ . Which of the following is true?

• After 20 days, there are 49 ants in the colony.

• After 49 days there are 20 ants in the colony.

• The amount of ants times 20 is 49.

• After 20 days the amount of ants remaining decreases by 49.

James' 70 in. giant peach doubles in size every week, and the size can be modeled by  $P=70\left(2\right)^t$ , where t is in weeks. How big is the peach after 5 weeks?

• 72 in.

• 2,240 in.

• 700 in.

•  $2.4\times10^{12}$ in
  

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to follow the equation  $P=4000\left(1.25\right)^t$ , where t is in months. How many mosquitoes will there be after 4 months?

• 9766

• 9006

• 9765

• 5433

Which equation is an exponential equation?

• y = ae^x

• y = ln x

• y = mx + b

The population of the United States was 248,718,301 in 1990 and was projected to grow following the model  $P=248718301\left(1.08\right)^d$ , where d is in decades (10 years). Predict the population, to the nearest thousand, for the year 2018.

• 133,156,000 people

• 1,289,647,000 people

• 308,528,000 people

• 55,448,000 people

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing following a model of  $A=250\left(1.03\right)^t$ , where t is in months. How many people will attend by the end of a year?

• 356

• 265

• 5825

• 1329

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour ( $B=2^t$ ), how many hours will it take to have 16,384 bacteria?

• 10

• 12

• 14

• 16

Which function represents an exponential function?

• $f\left(x\right)=\frac{1}{2}x^2-5$

• $f\left(x\right)=5\cdot\left(\frac{1}{2}\right)^x$

• $f\left(x\right)=\frac{1}{2}x-5$