Question

Solution for 5 b)
I know that
t(90 000)=a • square root of 120 000- 90 000
How do I find the thickness?

Answer 1

We need the value of $a$ from the first question. The initial thickness is 12mm, there "initial" means that the car has been driven for 0 kilometers. So, we know that

$f(0)=12 \iff a\sqrt{120000-0}=12 \iff a=\dfrac{12}{\sqrt{120000}}=\dfrac{12}{200\sqrt{3}}$

Now, the second questions asks for the thickness after the car has driven 90000 km. So, we simply need to plug $k=90000$ in the equation to get

$f(90000)=\dfrac{12}{200\sqrt{3}}\sqrt{120000-90000}=\dfrac{12}{200\sqrt{3}}\sqrt{30000}=\dfrac{12}{200\sqrt{3}}100\sqrt{3}=6$