Question 1138238
here's what i get.


general form for exponential function is y = ab^x.


when x = 1, you get ab^1 = 40
when x = 2, you get ab^2 = 16
when x = 3, you get ab^3 = 6.4
when x = 4, you get ab^4 = 2.56


if you take ab^2 and divide it by ab^1, you get .4
if you take ab^3 and divide it by ab^2, you get .4
if you take ab^4 and divide it by ab^3, you get .4


take a look at any one of these and you'll see that a drops out of the equation each time.


for example:


ab^4 / ab^3 = 2.56 / 6.4 = .4


this results in ab^4 / ab^3 = .4


the a in the numerator and the a in the denominator cancel out and you are left with b^4 / b^3 = .4


since b^4 / b^3 is equal to b^(4-3), you are left with b = .4


therefore, your equations become:


a * .4^1 = 40
a * .4^2 = 16
a * .4^3 = 6.4
a * .4^4 = 2.56


simplify to get:


a * .4 = 40 which means a = 100.
a * .4^2 = 16 becomes a * .16 = 16 which means a = 100
go down the line and a will be 100 each time.


your exponential equation in the form of ab^x becomes 100 * .4^x.


you can graph this function as shown below.


<img src = "http://theo.x10hosting.com/2019/040421.jpg" alt="$$$" >


the graph shows that the solution is correct.