2.6 Modelling skills Quiz

1. The value of an asset is modelled by $V=ka^t$. It is 50 at $t=0$ and 400 at $t=3$. Find $a$.

• A. $8$
• B. $3$
• C. $2$
• D. $350$

2. Which is the main danger of extrapolating a model?

• A. The model has too many parameters
• B. The GDC cannot evaluate the model
• C. The graph looks untidy
• D. The model may be unreliable outside the range of the data

3. To fit $y=ax^2+bx+c$ through three given points you need to solve:

• A. three linear equations in $a$, $b$ and $c$
• B. one quadratic equation in $x$
• C. two equations in $a$ and $b$ only
• D. an exponential equation

4. A model $f(t)=ka^t$ has $f(0)=120$. What is $k$?

• A. $1$
• B. $a$
• C. $120$
• D. $f(1)$

5. The temperature of a cooling object falls quickly and then levels off. Which model is best?

• A. $T=mt+c$
• B. $T=ka^{-t}+c$ with $a>1$
• C. $T=at^2+bt+c$ with $a>0$
• D. $T=a\sin(bt)+d$