When t 0 , the function F which maps t ↦→ t^3 (with domain and codomain all real numbers ℝ) is increasing
at an increasing rate. (Think of the variable t as denoting time.)
Show that this function is not exponential by showing that the ‘doubling time’ is not constant. More precisely,
for which t1 do we have F(t1) = 2 ; hence how long does it take to go from F(1) = 1 to F(t1) = 2 ?
Next, find t2 such that F(t2) = 4 and find the time required to go from F(t1) = 2 to F(t2) = 4 .
Do you obtain the same result? Is the doubling time increasing or decreasing?

Question

When t > 0 , the function F which maps t ↦→ t^3 (with domain and codomain all real numbers ℝ) is increasing
at an increasing rate. (Think of the variable t as denoting time.)
Show that this function is not exponential by showing that the ‘doubling time’ is not constant. More precisely,
for which t1 do we have F(t1) = 2 ; hence how long does it take to go from F(1) = 1 to F(t1) = 2 ?
Next, find t2 such that F(t2) = 4 and find the time required to go from F(t1) = 2 to F(t2) = 4 .
Do you obtain the same result? Is the doubling time increasing or decreasing?