Growth or Decay?
Does the following equation represent exponential growth or decay?
y=2^x
exponential growth
The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the population of the town after 9 years. Round to the nearest person.
38300(1.012)^9=42641
Consider the equation below. What is the initial value?
y=250(1.2)^t
250
Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.
y=422000(1.12)^t
Simplify:
6tv^0
6t
Does the following equation represent exponential growth or decay?
f(x)=100(0.5)^x
$1,200 is invested at an annual rate of 3.2%. How much money will the account have after 12 years? Round to the nearest cent.
1200(1.032)^12=$1751.21
Consider the equation below. What is the growth factor?
y=250(1.2)^t
1.2
Write an exponential growth function to model the situation. The population of Baconburg starts off at 20,000 and grows by 13% each year.
y=20000(1.13)^t
Simplify:
4^2x^-2
4^2/x^2 or 16/x^2
Does the following equation represent exponential growth or decay?
y=100(1.4)^x
exponential growth
The population in the town of Deersburgh is presently 42,500. The town has been growing at a steady rate of 2.7%. What will the population of the town be in 5 years? Round to the nearest person.
42500(1.027)^5=48556
Consider the equation below. What is the growth rate (as a percent)?
y=250(1.2)^t
20%
The fish in a local lake are declining at an annual rate of 1.5%. Their current number is estimated at 2500. Write an equation to model the decreasing number of fish.
y=2500(0.985)^t
Simplify:
4x^-2g^3
(4g^3)/x^2
Does the following equation represent exponential growth or decay?
f(x)=7(0.94)^x
exponential decay
The value of a car was $22,000 when it was purchased. The car depreciates (decreases in value) at a rate of 19% per year. How much will the car be worth in 8 years? Round to the nearest cent.
22000(1-0.19)^8=$4076.64
Consider the equation below. What is the decay factor?
y=9.8(0.35)^t
0.35
Write an exponential growth function to model the situation. Your starting annual salary of $64,000 increases by 3% each year.
y=64000(1.03)^t
Simplify:
(4^-2x^-5y^-9z^-3)^0
1
Does the following equation represent exponential growth or decay?
f(x)=-350(1)^x
neither
The value of a stock when purchased is $10 a share. However, over the past 5 days the price went down at a constant rate of 4%. How much is the stock worth now? Round your answer to the nearest cent.
10(1-0.04)^5=$8.15
Consider the equation below. What is the decay rate (as a percent)?
y=0.8(0.77)^t
23%
The squid in the magic forest lake were declining at an annual rate of 5.5%. Their current number is estimated at 50,000. Write an equation that represents this situation.
y=50000(0.945)^t
Simplify:
(x^-2y^2)/(b^-4c^4)
(b^4y^2)/(x^2c^4)