In this task you will be presented with a series of exercises where you will apply the properties of the functions to solve problems and you will be able to:

plot a data set with an exponential or logarithmic function;

solve exponential and logarithmic equations, and

calculate compound interest and effective rate.

Note: In the case that the result is decimal, you will round it to two decimal places.

1. Suppose a physician is monitoring cancer cells in a patient in order to initiate curative treatment before the count reaches 60,000. The data is observed in the following table:

Time in days Cell count

0 597

2 893

4 1339

6 1995

8 2976

10 4433

12 6612

14 9865

16 14719

18 21956

20 32763

On a Cartesian plane, plot the data set.

2.Solve the following equation using the corresponding properties: 3^x+1 = 81.

3.Solve the following equation using the corresponding properties: log₃ (4x-7) = 2.

4.Suppose $ 1,000 is deposited into a savings and loan account that pays 8% interest compounded semi-annually. Use compound interest to calculate the following:

a.How much money will you have saved?

b.How much will be owed after 2 years?

5. Celene invests $ 5,000 in a bank at 5.15% compounded annual interest each quarter. Use compound interest to determine what the annual percentage return is.