IB Mathematics Applications & Interpretation Topic…

Let $\log_{10} p=m$ , $\log_{10} q=n$ and $\log_{10} r=k$ .

Write $\log_{10} \frac{p^{3}\sqrt[3]{q^{2}}}{r^{4}}$ in terms of , and .

Lengths in this problem are measured in centimetres. Consider the function $r(x)=1+\sqrt{x}$ , defined for . A candle is formed by rotating the region between the curve and the -axis through about the -axis.

A flare's height is modelled by $h(t)=-t^3+7t^2+2t+1$ , where is in metres and is in seconds. In the first two parts, use technology where appropriate.

Consider the function $h(x)=\ln m-\ln((x-1)(5-x))$ , defined on the interval , where .

Consider the function $g(x)=\ln\big(k(12x-3x^2)\big)$ , defined on the interval , where .

Hence write $\frac{p^{3}\sqrt[3]{q^{2}}}{r^{4}}$ in terms of $m$ , $n$ and $k$ .

the total volume of the candle.

As the candle burns, the volume $W$ cm $^3$ of wax remaining after $t$ hours is modeled by $W=\frac{68\pi}{3}e^{-0.25t}$ . the time elapsed until half the candle remains.

Find the time when the flare hits the ground, giving your answer correct to three significant figures.

A signal reading is modelled by $P(u)=u^3-4u^2-11u+20$ . Write down an equation whose solutions are the $u$ -values for which the signal reading is $8$ , and solve it.

The cost of a subscription is modelled by $C(t)=240(1.09)^t$ , where $C$ is in dollars and $t$ is in years. Find the value of when the cost reaches .

Hence the first whole year for which the cost exceeds $600$ .

IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

IB Mathematics Applications & Interpretation AHL 1.9—log Laws Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 1.9—log Laws Questionbank