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Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e^-0.05tInitially, M₀= 300e⁰=300 x 1 = 300When the substance mass has decreased t...

e^3x differentiates to 3e^3x as you multiply the function e^3x by the derivative of the inside function 3x. 3x differentiates to 3, so the answer is 3 multiplied by e^3x. The derivative of a natural log f...

In differentiation, your goal is to reduce the power of the terms that you're differentiating with respect to (in this case, x).The method for doing this is:Multiply the power of your x term by its coeffi...

First we need to factorise the numerator into two expressions. We can see one expression must start (3x + ?) and the other therefore must hold (x + ?), we know this because the two bracke...

First step: n=1 we have 8¹ -1=7 which is divisible by 7. Assumption step: 8^k-1 is divisible by 7. Induction step: Using the previous step we have that 8^k-1=7x. So 8^k<...