Answer:
○[tex]\displaystyle \$885,78[/tex]
Step-by-step explanation:
This graph indicates Exponential Growth, so you would use this formula:
[tex]\displaystyle y = ab^x; from\:y = a[1 + r]^x[/tex]
... in which
Growth 'Rate' = r
[tex]\displaystyle 1 + r = b[/tex]
time, in years = x
Initial Amount = a
[tex]\displaystyle y = 500[1,1]^x \\ \\ y = 500[1 + 0,1]^x[/tex]
The growth rate is [tex]\displaystyle \frac{1}{10}.[/tex]Now, all you do is plug each x-value [year-value] into the function to make sure our growth rate is authentic:
[tex]\displaystyle y = 500[1,1]^6; 500[1,771561] = y; 885,7805 = y; 885,78 ≈ y \\ y = 500[1,1]^5; 500[1,61051] = y; 805,255 = y; 805,26 ≈ y \\ y = 500[1,1]^4; 500[1,4641] = y; 732,05 = y \\ y = 500[1,1]^3; 500[1,331] = y; 665,5 = y \\ y = 500[1,1]^2; 500[1,21] = y; 605 = y \\ y = 500[1,1]^1; 500[1,1] = y; 550 = y \\ y = 500[1,1]^0; 500 = y[/tex]
We NOW KNOW that our growth rate is genuine, therefore by the sixth year, Mia will have approximately [tex]\displaystyle \$885,78[/tex]in her deposit account.
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