The population (in millions) of a certain country can be approximated using the following function;
P(x)=40 ( 1.02)^x
where x is the number of years after 2000. which of the following calculations will tell you what the population can be expected to reach 200 million?

Question

The population (in millions) of a certain country can be approximated using the following function; 
P(x)=40 ( 1.02)^x 
where x is the number of years after 2000. which of the following calculations will tell you what the population can be expected to reach 200 million?

zmtgaminghd · Answer

279,378

cutiecomittee123 · Answer

oh well there are options 
ln(5/1.02)
ln(5)/ln(1.02)+2000
ln(5/1.02)+2000
ln(5)/ln(1.02)

campbell_st · Answer

ok so let P(x) = 200

so 

$$200 = 40\times (1.02)^x$$

divide both sides of the equation by 40

$$5 = (1.02)^x$$

take the log of both sides... and apply the log law for powers
and you'll get the answer

campbell_st · Answer

the log law for powers is 

$$\log(x^a) = a \times  \log(x)$$

cutiecomittee123 · Answer

so log(5)=log(1.02)^x  ??

campbell_st · Answer

yes... so now what happens to x, with you use the log law for powers

cutiecomittee123 · Answer

can you show me how that works?

campbell_st · Answer

ok

$$\log(5) = x \times \log(1.02)$$

now you can solve for x

cutiecomittee123 · Answer

got it! so just divide log(5) by log(1.02)

campbell_st · Answer

that's correct

cutiecomittee123 · Answer

so the answer is d, in the options i have above?

campbell_st · Answer

yes

cutiecomittee123 · Answer

Can you help me with another one?

cutiecomittee123 · Answer

@campbell_st

campbell_st · Answer

just post a new question, there are lots of people who can help, I'll look at it if I have time

cutiecomittee123 · Answer

Okay