A small business owner made $40,000 the first year he owned his store and made an additional 7% over
the previous year in each subsequent year. Find how much he made during his fourth year of business.
Find his total earnings during the first four years.

Question

rational · Answer

we may use $n$th term of geometric sequence formula to find the amout he makes during fourth year : 

$$\large a_n = a_1r^{n-1}$$

rational · Answer

here $r = 1.07$ and $a_1 = 40,000$

nnesha · Answer

don't we have to use this one ??
$$\rm A =P(1+\frac{ r }{ n })^{nt}$$
or A = p(1+r)^t

rational · Answer

that also works!

rational · Answer

otherwise work each term manually as there are only four terms

rational · Answer

first year : 40,000
second year : 40,000 + (7% of 40,000) = ?

nnesha · Answer

$$\huge\rm a_4= 40000(1.07)^{4-1}$$
49,001.72

rational · Answer

that looks good!

nnesha · Answer

what about this one 
"A small business owner made $\large\rm{$3000}$ the first year he owned his store and made an additional $$14%$$ over
the previous year in each subsequent year. Find how much he made during his fourth year of business.
Find his total earnings during the first four years.
$$a_4=30000(1.14)^{3}$$
=4444.32 is it right ??

rational · Answer

this looks more like arithmetic sequence right ?
because the growth amount is same each year :  $14

nnesha · Answer

14%**

rational · Answer

then you're correct !

nnesha · Answer

but answer choices are 
a) $33,745.92 , 127,393.92 <----------------A is right answer :o
b) $82,230.00 ; $213,120.00
c)$1.92; $31249.92
d)$115248.00:$328,368.00

rational · Answer

is the first year amount $3,000  or $30,000 ?

nnesha · Answer

$30,000

rational · Answer

Okay what about the growth factor ? is it 14% or just 4% ?

nnesha · Answer

_-_ 4% ;p

nnesha · Answer

thanks!!

rational · Answer

np :)