If an object's speed increases by ten percent each second, we can analyze its speed using exponential growth. Let's assume the initial speed of the object is denoted as v₀.
After one second, the speed of the object will increase by ten percent, which can be expressed as:
v₁ = v₀ + 0.1v₀ = 1.1v₀
After two seconds, the speed will increase by ten percent again:
v₂ = v₁ + 0.1v₁ = 1.1v₁ = 1.1(1.1v₀) = 1.21v₀
After three seconds:
v₃ = v₂ + 0.1v₂ = 1.1v₂ = 1.1(1.21v₀) = 1.331v₀
As you can see, the speed increases exponentially. We can generalize this pattern:
vₙ = (1 + 0.1)ⁿv₀
where vₙ represents the speed at time n seconds and v₀ is the initial speed.
In this case, since the speed increases by ten percent each second, the growth factor is 1 + 0.1 = 1.1.
If you want to calculate the speed at a specific time, substitute the value of n into the equation along with the initial speed (v₀).