We are asked in this problem to determine the expression of an exponential function given the data above. The standard form of an exponential function is expressed as y = a^x + b was a is the base constant and b is another constant. In this case, a is given to be equal to 1/2. since the graph is said to be shrunk down to 3/4 then the initial expression would have to be y = 3/4*(1/2)^x + b. b is determined through the given asymptote in the problem. An asymptote is an axis or the line in which the graph approaches but never touches. b is equal to -4. In this case, the overall expression is y = 3/4 *(1/2)^x - 4.
