Respuesta :
We are told that the first week Lucy earns $50. We want to calculate the second week's earnings. Since earnings increase 10% every week, we will calculate 10% of 50 and then add it to 50. To calculate 10% of a number, we simply multiply the number by 0.1.
Then, the 10% of 50 would be
[tex]50\cdot0.1=5[/tex]Now we add this quantity to 50. This would give the earnings of the second week. So, the earnings of the second week would be
[tex]50+5=55=50+50\cdot0.1=50\cdot(1+\frac{10}{100})[/tex]From here, it is important to note that to increase a quantity by a 10% we simply multiply the quantity by the number (1+10/100). So, to calculate the earnings of week 3, we simply multiply the earnings of week 2 by (1+10/100)
This would be
[tex]50\cdot(1+\frac{10}{100})\cdot(1+\frac{10}{100})=50\cdot(1+\frac{10}{100})^2[/tex]Finally, we repeat the process for week 4, This would give
[tex]50\cdot(1+\frac{10}{100})^2\cdot(1+\frac{10}{100})=50\cdot(1+\frac{10}{100})^3[/tex]So we have
[tex]50\cdot(1+\frac{10}{100})^3=66.55[/tex]To calculate the earnings of all 4 weeks, we simply add this numbers, so we have
[tex]50+50\cdot(1+\frac{10}{100})+50\cdot(1+\frac{10}{100})^2+50\cdot(1+\frac{10}{100})^3=232.05[/tex]So in 4 weeks, Lucy earns 232.05
