exponentials and logs yr12 maths

on the same graph, draw the following curves:

y = (1/2)^x

y = 2^x

y = -2^x

y = -(1/2)^x

draw a graph for y = ln x or any log x

differentiate y=e^x

differentiate y=e^kx

what is ln(e) = ?

1

what are the 3 log laws

can the input of a log be -ve (e.g can I have this ln(-1). is this possible?)

no

for us to use the log law where u multiply them inside a log (when they are being added), what must be true about their coefficients and bases

the bases must be the same

the coefficients must be the same

for example u can do 2ln(x) + 2ln(3x) → 2ln(3x²)

what are the only 2 acceptable models when talking about exponential models?

if a model is within ________% of the actual/observed value, we can say it is a good model. otherwise, is unreliable

within 10%