Hey guys I'm new here. How's everyone doing? I just finished doing a bunch of log problems. If you find any faults, please tell me. This test counts for a lot, and every correct answer is worth big.

I wrote out all the questions, and at the bottom of each I wrote my answers in bold. Please guide me guys. I need to ace this.

1-A bacteria divides into 4 new cells every 20 minutes. If the bacteria reproduces for x hours, find the

exponential equation that represents the increase in population as a function of time.

I foundy= 12^x

2- Simplify:

A- (2/3)^2X+3 = (27/8)^3X-2

I foundx=0,27

B- 3^x+3= 13574

I foundx= 5.6617

3- Find the inverse of the following function: f (x)= log base5(3-x)

I foundy= -5^x + 3

4- For the following function f(x)= 3 (1/2)^4x-1 + 5, State whether the statements are true or false. Correct the false ones.

A. It is decreasing

B. The ordinate is 8

C. The equation of the asymptote is y=5

D. It is always positive

E. It has no abcissa at the origin

I wrotetrue for A, C, D and E, and I wrote the ordinate is 11 for B

5- Find the equation of the following log function with an asymptote of x= -5.625 and passing through the point (10,3)

I foundy= log2.5 (x+5.625)

6- Martha brought a bond for 1500.00$ at an annual rate of 4.8%, compounded semi annually. Find the rule that

describes the value as a function of the number of years. Using the rule, find the value in 10 years.

I found the rule was y= 1500. 1.024^2x, so in 10 years

y= 1500 . 1.024^20=1901,47$

7- The following rule is used for calculating the number of years (y) it takes for a bond to reach a certain amount (x)

y= 96.64logx - 460.34

Calculate how much time it would take to reach 65000 and 85000.

I put in 65000 and 85000 for x, and got4.78 and 16.04.

8. Find the value of the following expression:

8(log4 32 + log2 8) - (log2 16)^2

I found28

Thanks in advance guys!