Question

(1 point) Without using a calculator, match each exponential function with its graph | Choose-e0.06t 0.5t Choose e Choose ▼ e-0.02t Choose ▼|e-02t (III》 IV) (Click on graph to enlarge)

Answer 1

We can easily guess the graphs if we get an idea of the slopes of each of the function.

We know that slope is nothing but the first order derivative of the function. So for e^x the slope will be x.e^x that is the value of x will determine the magnitude of the slope and the positive and negative sign would tell about the direction.

So e^0.5t would give us the highest slope among all, so it would be the steepest among all hence it is (I).
Similarly e^-0.2t will give the lowest slope in the first quadrant, hence it is (IV).
Similarly e^0.06t will be (II) and e^-0.02t is (III).