algebra 2 project

Solving Exponential Equations

100

16^{5X+7} = 64^{3X+4}

x = -2

200

9^{6X-3} = 3^{10X+6}

x = 6

300

8^X+3 = 2^X-3

x = -6

Exponential Functions

100

On a farm, there are 100 cows. They have reportedly been increasing in population by 10% per year. If this continues on for 25 years, how many cows will there be on the farm? (round down)

There will be 1,083 cows on the farm.

200

x = (1/5)^-3

x = 125

300

If I have a brand new car worth $30,000 and it decreases in value by 12.5% every 5 years, how much will it be worth in 15 years? (round to nearest hundredth)

The car is worth $20,097.66.

Exponential Growth/Decay Models

100

Danny puts $10,000 into his bank account. They told him that there is a 12% yearly interest rate. He leaves the money in the account for 7 years. How much has he gained?

He has gained $12,106.81.

200

Johnny deposited $15,000 into the bank. They gave him a 5% interest rate for his deposit every year. If Johnny leaves the money alone for 3 years how much would he have? (round to nearest hundredth)

He will have $17,364.38.

300

Larry deposited $1,000 into the bank. He spends 5% of his cash every month. How many months does it take him to below $500?

It takes him 14 months.

Solving Logarithmic Equations

100

log of 3 (81) = x

x = 4

200

log of 7 (343) = x

x = 3

300

log of 9 (729) = x

x = 3