A city’s current population is 500,000 people. It is growing at a rate of 2.5% per year. The equation p=500,00(1.025)^x models the city’s population growth where x is the number of years from the current year. In approximately how many years will the population be 640,000?

Question

anonymous · Answer

substitute p= 640,000 in the given eq

anonymous · Answer

$$p=500,00(1.025)^x \rightarrow 640,000=500,00(1.025)^x$$
$$\frac{640,000}{500,00}=(1.025)^x \rightarrow \frac{64}{5}=(1.025)^x$$
$$12.8=(1.025)^x \rightarrow \frac{128}{10}=(\frac{1025}{1000})^x$$
$$\frac{2^7}{10}=(\frac{41}{40})^x$$
solve it further for x

anonymous · Answer

would it be 20 years? @dpasingh

ash2326 · Answer

how did you solve this?

ash2326 · Answer

@jessy1289

anonymous · Answer

is it 20 years ? @ash2326

ash2326 · Answer

@jessy1289 did you use a calculator or logarithm table?

anonymous · Answer

no

ash2326 · Answer

then how did you solve?

ash2326 · Answer

We have 
$$\frac{128}{10}=(\frac{41}{40})^x$$
We would need to use logarithms here.  Have you studied that? @jessy1289

anonymous · Answer

no but im guessing its 20 years

ash2326 · Answer

That seems like a cool guess, but if you  solve it you'd be surprised.

ash2326 · Answer

Just google  this
log(128/10) / log( 41/40)

anonymous · Answer

103? @ash2326

ash2326 · Answer

right