Edexcel AS Level Maths: 14.3 Exponential Modelling 

anything to do with rate is usually indicating to a differentation. As when we differentiate we are finding the gradient which is the same as the rate of the change of a curve

I completed the question without differentiating and got the same answer. In the original equation, I substituted 8 into t, which gave me approximately 3533.76. Then I divided by 8 to get 441.72. Hope this helps

Hi! I think because 100x0 belongs to the exponential e. As e^-0.5t belongs to the 100 due to -100e^-0.5t so only 100 will be affected by the 0 hence 300-(100x0) = 300-0 = 300. If you have started year 2 maths yet just think of it when you’re giving the value of theta for small angle approximations theta tends to 0 aswell as any number attached to the theta symbol. E.g, when it’s 3-2θ, -2θ tends to 0 therefore θ tends to 3. I hope this helps with your question!☺️

Sorry I forgot to mention that he basically subs in e^-0.5t as zero in the equation sorry I missed that out!