15% decrease means multiply by \( 0.85 \) (M1)

\( 35000 \times 0.85 = 29750 \) (A1)

Answer: $29,750 [2 marks]

After first year, value is $29,750; then 11% decrease yearly (multiply by \( 0.89 \)) for 9 years (M1)

\( 29750 \times 0.89^9 \) (A1)

\( 0.89^9 \approx 0.351787 \) (A1)

\( 29750 \times 0.351787 \approx 10423.1030 \) (A1)

Rounded to nearest dollar (M1)

Answer: $10,423 (A1) [5 marks]

10% of $35,000 is $3,500; solve \( 29750 \times 0.89^{n-1} < 3500 \) (M1)

\( 0.89^{n-1} < \frac{3500}{29750} \approx 0.117647 \) (A1)

Method 1 (Logarithms):

Taking logarithms: \( (n-1) \ln 0.89 < \ln 0.117647 \) (M1)

\( \ln 0.89 \approx -0.116533 \), \( \ln 0.117647 \approx -2.13860 \) (A1)

\( n-1 > \frac{-2.13860}{-0.116533} \approx 18.35 \implies n \geq 20 \) (A1)

Verify: \( n=19 \), \( 0.89^{18} \approx 0.1276 \), \( 29750 \times 0.1276 \approx 3797 > 3500 \) (M1)

\( n=20 \), \( 0.89^{19} \approx 0.1136 \), \( 29750 \times 0.1136 \approx 3380 < 3500 \) (A1)

Method 2 (Finance App):

Use finance app with \( I\% = -11 \), \( PV = \mp 29750 \), \( FV = \pm 3500 \) (M1)

Solve for \( N \approx 18.3643 \) (A1)

Smallest integer \( n \geq 19.3643 \implies n = 20 \) (A1)

Answer: \( n = 20 \) (A1) [8 marks]