miguel invested $400 in a bank account that pays interest. the accounts value over time, in x years, is…

miguel invested $400 in a bank account that pays interest. the accounts value over time, in x years, is given in the table. which exponential function models the data? round the numerical values to the nearest hundredth. $f(x)=1.41(30.69)^{x}$ $f(x)=37.74(396.48)^{x}$ $f(x)=390.60(1.41)^{x}$ $f(x)=401.19(1.08)^{x}$

miguel invested $400 in a bank account that pays interest. the accounts value over time, in x years, is given in the table. which exponential function models the data? round the numerical values to the nearest hundredth. $f(x)=1.41(30.69)^{x}$ $f(x)=37.74(396.48)^{x}$ $f(x)=390.60(1.41)^{x}$ $f(x)=401.19(1.08)^{x}$

Answer

Explanation:

Step1: Recall the general form of an exponential function

The general form of an exponential function is (f(x)=a(b)^{x}), where (a) is the initial value when (x = 0).

Step2: Check the initial - value for each function

For (y = f(x)=a(b)^{x}), when (x = 0), (f(0)=a).

  • For (f(x)=1.41(30.69)^{x}), when (x = 0), (f(0)=1.41\neq400).
  • For (f(x)=37.74(396.48)^{x}), when (x = 0), (f(0)=37.74\neq400).
  • For (f(x)=390.60(1.41)^{x}), when (x = 0), (f(0)=390.60\neq400).
  • For (f(x)=401.19(1.08)^{x}), when (x = 0), (f(0)=401.19\approx400) (rounded to the nearest hundredth).

Step3: Check another point

Let's check (x = 1). For (f(x)=401.19(1.08)^{x}), when (x = 1), (f(1)=401.19\times1.08=433.2852\approx436) (rounded to the nearest whole number).

Answer:

(f(x)=401.19(1.08)^{x})