Andy and Ena opened separate bank accounts that earn compound interest. Andy's account can be modeled by the function f(x)=275(1.06)x. Ena's account can be modeled by the function f(x)=115(1.09)x. Which statement about the functions is true? F. The beginhing balances cannot be determined, but Andy's account earns a higher annual interest rate than Ena's account. G. The beginning balances cannot be determined, but Ena's account earns a higher annual interest rate than Andy's account. H. Andy's account has a higher beginning balance, but Ena's account earns a higher annual interest rate of 9%.J. Andy's account has a higher beginning balance, but Ena's account earns a higher annual interest rate of 1.09%.

Question

Andy and Ena opened separate bank accounts that earn compound interest. Andy&#039;s account can be modeled by the function f(x)=275(1.06)x. Ena&#039;s account can be modeled by the function f(x)=115(1.09)x. Which statement about the functions is true? F. The beginhing balances cannot be determined, but Andy&#039;s account earns a higher annual interest rate than Ena&#039;s account. G. The beginning balances cannot be determined, but Ena&#039;s account earns a higher annual interest rate than Andy&#039;s account. H. Andy&#039;s account has a higher beginning balance, but Ena&#039;s account earns a higher annual interest rate of 9%.J. Andy&#039;s account has a higher beginning balance, but Ena&#039;s account earns a higher annual interest rate of 1.09%.

sonSnubsreose6v · Accepted Answer

Step 1  The amount(A) in the account after x years can be calculated as below, where P is the principal and interest rate is r% and the time of deposit is x.  A=P(1+r100)x  Step 2  Write Andy’s and Ena’s account function as above function and find the beginning balance and interest rates.  For Andy F(x)=275(1.06)x  F(x)=275(1+6100)x  So, beginning balance =275  interest rate =6%  For Era F(x)=115(1.09)x  F(x)=115(1+9100)x  So, beginning balance =115  interest rate =9%  Hence, Statement (H) is True.  Andy’s account has higher beginning balance but Ena’s account earns a higher annual interest rate of 9%.

encolatgehu · Accepted Answer

Step 1Given,Andy and Ana’s account modeled by the function f(x)=275(1.06)x and f(x)=115(1.09)x.As we know, A=P(1+r100)t (i)Where A= Final AmountP= Initial Principal ValueR= RateT= timeStep 2The beginning the balance can be calculated by substituting x=0 as shown below:The beginning the balance of Andy =f(0)=275(1.06)0=275And the beginning the balance of Ana’s =f(0)=115(1.09)0=115So, the beginning balance of Andy is more than the beginning balance of Ana’s.Let the interest rate of Andy and Ana&#039;s be r1 and r2Now, rearranging the account function of Andy and Ana&#039;s as shown below:f(x)=275(1.06)x=275(1+0.06)x=275(1+6100)x (ii)and f(x)=115(1.09)x=115(1+0.09)x=115(1+9100)x (iii)Now, comparing the equation (ii) and (iii) with respect to the equation (i), we getr1=6 and r2=9Since, r1&amp;lt;r2 so the interest rate of Andy is less than the interest rate of Ana&#039;sStep 3Answer: The correct Option is H.

user_27qwe · Accepted Answer

The amount(A) in the account after x years can be calculated as below, where P is the principal and interest rate is r% and the time of deposit is x. A=P(1+r100)x Write Andy’s and Ena’s account function as above function and find the beginning balance and interest rates. For Andy F(x)=275(1.06)x F(x)=275(1+6100)x =275 interest rate =6% For Era F(x)=115(1.09)x F(x)=115(1+9100)x =115 interest rate =9% Hence, Statement (H) is True. Andy’s account has higher beginning balance but Ena’s account earns a higher annual interest rate of 9%.

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