The dollar value \( v(t) \) of a certain car model that is \( t \) years old is given by the following exponential function. \[ v(t)=29,900(0.84)^{t} \] Find the value of the car after 4 years and after 11 years. Round your answers to the nearest dollar as necessary. Value after 4 years: Value after 11 years:

To find the car's value after 4 years and after 11 years, we simply substitute \( t \) with 4 and 11 in the given function. For \( t = 4 \): \[ v(4) = 29,900(0.84)^{4} \approx 29,900 \times 0.497 = 14,853 \] For \( t = 11 \): \[ v(11) = 29,900(0.84)^{11} \approx 29,900 \times 0.076 = 2,272 \] So, rounding to the nearest dollar: Value after 4 years: **$14,853** Value after 11 years: **$2,272**