# Mathematics

1.Find the values of a and b for the polynomial f(x) = 2x^3 + ax^2 - 4x + b, given that f(x) is divisible by x+1 and x-3. Write f(x) in a factorised form.

Hint: consider f(-1) and f(3)

2. The population of a country is found to be growing continuously at an annual rate of 1.98% t years after 1 January 1960. The total population t years after 1 January 1960 is given by the formula P(t) = 120 x 10^6 e^kt

How many years after 1 January 1960 would it take for the population to reach 240 x 10^6?

3. The decay of a radioactive substance is modelled by M=Mo(sorry meant to be subscript zero) (10) ^-kt, where Mo is the initial of the substance, M is the mass remaining after t years, and k is a constant. If it takes 150 years for the substance to reach half of its original mass in, show that k = log2/150

© BrainMass Inc. brainmass.com October 16, 2018, 11:48 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/mathematics-269986

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems and provides students with a clear perspective of the underlying concepts.

Mathematics - Solving a Finite Mathematics Problem

I am trying to work these problems not quite sure of how to work them.

Find the equation of the line shown ...

A bank loaned $15,000, some at an annual rate of 16% and some at an annual rate of 10%. If the income from these loans was $1800, how much was loaned at 10%?

Write the augmented matrix of the system ...

2x1 -3x2 + x3 = 0 x1 - x2 - 2x3 = -2 -5x1 + x2 = -4

(Please see the attached file)

View Full Posting Details