square footage has gone from 1500 sqr. ft to 2330 sqr. ft from 1970 to 2004

Using the model A= Pe^rt

r = .008

According to this model which year will the average home exceed 3200 sqr. ft

Question

square footage has gone from 1500 sqr. ft to 2330 sqr. ft from 1970 to 2004 

Using the model A= Pe^rt 

r = .008 

According to this model which year will the average  home exceed 3200 sqr. ft

campbell_st · Answer

well using the model Initial footage P = 1500 r = 0.008 and A = 3200 you need to find t

$$3200 = 1500 e^{0.008t}$$

$$e^{0.008t} = 3200/1500$$

take the ln of both sides

$$0.008t = \ln(3200/1500)$$

then 

$$t = \ln(3200/1500)/0.008$$

anonymous · Answer

the answer is the year 2028 but i cant figure out how to get to the answer :( ugh so confused

campbell_st · Answer

once you find t... add it the value to the starting year 1970

anonymous · Answer

hmm, when i do the equation i get 95? so added to 1970 i get 2065....

campbell_st · Answer

make sense

anonymous · Answer

but the real answer is 2028 so no it doesnt make sense .....:(

campbell_st · Answer

well the problem with your question is your r value... its not 0.008. 

you need to find r 1st

$$2330 = 1500e^{r \times 34}$$

solving for r will give r = 0.01295

using this value for r rather than 0.008 and the  method above you'll find t = 58