Each year francesca earns a salary of 2% higher than her previous years salary. in her first 5 years at this job, she earned a total of 187,345. what was francesca salary in her 1st year at this job

$36,027.9

Step-by-step explanation:

Lets say her salary in the first year is s1. So, in the second year her salary will be 2% higher than x, this is, s1 + s1*0.02, so:

s2 = s1 + 0.02s1 = 1.02s1

Then in year 3 it will be s2 plus a 0.02 increase:

s3 = s2 + 0.02s2 = 1.02(s2) = 1.02 (1.02 s1) = 1.02^2(s1)

Then the same for s4: s3 salary plus the increase.

s4 = s3 + 0.02s3 = 1.02(s3) = 1.02 (1.02 s2) = 1.02(1.02*1.02 s1) =1.02^3(s1)

Finally for the 5th monts:

s5 = 1.02(s4) = 1.02^4(s1)

We know that s1+s2+s3+s4+s5 = 187,345

Lets replace all the salaries by its value depending on s1

s1 + 1.02s1 + 1.02^2(s1) + 1.02^3(s1) + 1.02^4(s1) = 187,345

We can add to the first term a s1^0 as it is eqaul to 1

s1 + 1.02s1 + 1.02^2(s1) + 1.02^3(s1) + 1.02^4(s1) = 187,345

Lets get 1s1 out as common factor:

s1 (1 + 1.02^1 + 1.02^2 + 1.02^3 + 1.02^4) = 187,345

s1 *5.20 = 187,345

Divide both sides by 5.20

s1 = 36,027.9

So, her salary in the 1st month was approximately $36,027.9