Which of the following is false for an exponential growth function y = c(1 + r)t? a. when c > 0, the function decreases from left to right c. the graph of this function will be identical to the graph of y = abx, if a = c and b = 1 + r b. the function has a y-intercept of (0, c) d. if c > 0 and r > 0, then the graph will only have positive y-values.  

your choices area. when  , the function decreases from left to right b. the function has a y-intercept of  c. the graph of this function will be identical to the graph of  , if    and  .d. if c > 0 and r > 0, then the graph will only have positive y-values.    choice a is wrong.if you look at choice a: if  , then c is positive.when c is positive, then the only other thing that can make the exponential function be increasing or decreasing is  .they did not put any restrictions  for  , meaning this is a claim that applies for all possible values or r.  but if we say that  and , our function would look likewhich is an increasing function, from left to right. the growth factor of 1.5 increases the initial value of 10 as t goes up.  we showed a counterexample—an example when the claim does not work. so we can say this is false.choice a is false.if you look at choice b: the y-intercept is where the graph of the function intercepts the y-axis. since the y-axis is at t=0, plugging in yieldsbecause anything to the power of 0 is 1. since when  , the point  is on the graph of  .so choice  b is true.if you look at choice c: it is just a substitution. so it is also true.if you look at choice d: c > 0 means that there will be no reflections in the horizontal axis. we have no vertical translations either.all exponential functions that have no vertical translations or reflections in the horizontal axis will have only positive y-values. raising a real number to an exponent will never result in a negative numberso d is true.the only thing false is a. so a.

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