Problems on Exponential and logarithm, some of the most important concepts in mathematics, are presented along with detailed solutions.

Problem 1:
where t is in years and t = 0 corresponds to 1980. In 1990, the population was 10000. Find the value of the constant a and approximate your answer to 3 decimal places.
Problem 2:
where k is a constant and t is the time in years with t = 0 corresponding to the year 2000. Find constant k so that the two populations are equal in the year 2020 and approximate your answer to 3 decimal places.
Problem 3:
where I is the sound intensity in watts per centimeters squared. Determine the level in decibels of a sound with intensity I = 10^{ 8} watts/cm^{ 2}.
Problem 4:
Problem 5:
where N is the number of people infected by the virus after t days. How many days it takes for 2000 people of this city to be infected with the virus? (approximate your answer to 3 decimal places).
Problem 6:
where A_{ o} is the initial amount, k is a positive constant and t is the time in days. Find a formula for the half life of the material.
Problem 7:
where a, b and k are constants. Solve the above equation for t.
Problem 8:
where a is a positive constant depending on the values of the electronic components included in the electrical circuit and V_{ o} is the initial voltage. Find t for which V(t) is equal to 50% of V_{ o}.
Problem 9:
where P_{ o} is the output power and Pi is the input power of the system. Find the input power Pi if the output power is equal to 10 mw and the signal ratio in decibels is equal to 10 decibels.
Problem 10:
where E is the voltage applied to the circuit, R is the resistance and L is the inductance. Express i in terms of E and R when t = L/R. More math problems with detailed solutions in this site. 