491: Discuss the Errors, part 2

This question is from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with it?

How would they fix it?



source.

451: Growth Rate

Population of organism after n minutes is $P(n) = k*9^{(\frac{n}{2})}$.
What is the growth factor?

... algebraically stated, what is the ratio of P(t+1):P(t)?

Source:

#SATPrep Population of organism after n min is P(n)=k•9^(n/2) P( t+1):P(t)? #mathchat 

— David Marain (@dmarain) April 30, 2015

403: An Exponent Question

Considering the tweet below, which mental path do you think is easiest for beginning students?  (Analytical, numerical, graphical, algebraic?)

Would you give a different hint to beginning students than to advanced students?

#mathchat #SATPrep Will the average of 2^48 & 2^50 be <,>, or = 2^49?
Hint: Think graphically!
Now show the actual avg is 1.25×2^49.
— David Marain (@dmarain) March 18, 2015

365: Exponential Fun

If a and b are both positive integers, $a^{a - b}=10^6$,

list all possible ordered pairs (a,b).

What are a couple of different ways to approach this nugget?

What are the "obvious" answers that everyone will miss?

If a,b pos int's, a^(a-b)=10^6, list all possible ordered pairs (a,b)?
Ans:(10,4);(100,97);(1000,998); (1000000,999999)
— David Marain (@dmarain) January 3, 2015

318: Exponential Function

Is this enough information to find the equation?