2.2: Linear law graph: $\ln P$ against $t$

Draw the graph of $\ln P$ against $t$ on the grid below.

Use the graph to estimate the value of $P$ when $t = 2.2$.

Find the gradient of the graph and state the coordinates of the point where the graph meets the vertical axis.

Using your answers to part (iii), show that $P = ab^{t}$, where $a$ and $b$ are constants to be found.

Given that your equation in part (iv) is valid for values of $t$ up to 10, find the smallest value of $t$, correct to 1 decimal place, for which $P$ is at least 1000.