The table shows the prices for fruit items at a local farmer’s market. Katelyn purchased four pounds of apples, six navel orange

Detailed derivation:

dA/dt = 6 - 0.02A

dA/dt = -0.02 (A - 300)

Rearranging terms.

dA / (A - 300) = -0.02 dt

Integrate both sides.

ln(A - 300) = -0.02t + C

Isolate A.

A - 300 = Ce^(-0.02t)

A = 300 + Ce^(-0.02t)

Apply initial condition to determine C.

50 = 300 + Ce^(-0.02 × 10)

50 = 300 + Ce^(-0.2)

-250 = Ce^(-0.2)

C = -250e^(0.2)

A = 300 - 250e^(0.2)e^(-0.02t)

A = 300 - 250e^(0.2 - 0.02t)