can someone help me in this exponential and logarithmic function assignment

Question

An increasing exponential function y = a(b)^x and a decreasing exponential function y = c(d)^x intersect at the point (0,3)

 

 

a) Which characteristics of the functions are the same? [2] Which characteristics would be different?

b) Write one possible equation for each of the two functions. 

Answer 1

(a) The intersection point implies that the pair of x and y values (the coordinates (0,3)) satisfy both equations. So, if we plug x=0 into each equation, the y values will be the same for each equation. The intersection point is the y-intercept for both equations.

(b) Let's pick some values for a and b first to satisfy (0,3). b⁰=1 for all b, so a=3. Let b=2 (arbitrary value), then y=3(2)^x. This is an increasing function. The second equation has to be decreasing but y=3 when x=0, so c=3. I think y=c(d)^-x for the second equation, because, like the first equation, y=c(d)^x would also be increasing. So let d=5, y=3(5)^-x. This equation decreases exponentially.

y=3(2)^x and y=3(5)^-x are examples.