Hello mztoAt time , there are 40 spores.

After 1 week, , there are spores

After 2 weeks, , there are spores

... and so on.

After weeks, there are spores

So, if there are 2000 spores at time ,

, because the log (to base 10) of a number is the power to which you must raise 10 to get the number. (Do you understand this sentence? It's vital that you do, because you'll need it again in the second question - see below!)

weeks, or 11 days 21.4 hours.

We need to find D when .The astronomer johannes kepler determined that the time, D, in days, for a planet to revolve around the sun is related to the planet's average distance from the sun, k, in millions of kilometres. This relation is defined by the equation log D = (3/2)logk - 0.7. Estimate the period of revolution of uranus about the sun, given its distance from the sun. Uranus is 2854 million kilometres away from the sun

So

So is the power to which we must raise in order to get (see question 1). In other words:

days

(Note that you can probably do this calculation on your calculator in two ways: one is to enter 4.48318 and then press INV and LOG, and the other is to use the x^y button, entering 10 for x and 4.48318 for y.)

Grandad