(Rround to the nearest tenth.) e) Find the amount of time after which the value of the toy tractor will be \( \$ 1652 \). \( \square \) years (Round to the nearest tenth.) xample Get more help - Clear all F030) is based on Bittinger: College Algebra Graphs \& Models, 6e Digital Update
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Typically, this involves an exponential function. Assuming the value of the toy tractor changes according to an exponential model, we can use the formula: \[ V(t) = V_0 \cdot e^{rt} \] where: - \( V(t) \) is the future value of the toy tractor. - \( V_0 \) is Show more…
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A farmer depreciates a $\$ 120,000$ tractor. He estimates that the resale value $V(t)$ (in $\$ 1000$ ) of the tractor $t$ years after purchase is $80 \%$ of its value from the previous year. Therefore, the resale value can be approximated by $V(t)=120(0.8)^{t}$. a. Find the resale value 5 yr after purchase. Round to the nearest $\$ 1000$. b. The farmer estimates that the cost to run the tractor is $\$ 18 / \mathrm{hr}$ in labor, $\$ 36 / \mathrm{hr}$ in fuel, and $\$ 22 / \mathrm{hr}$ in overhead costs (for maintenance and repair). Estimate the farmer's cost to run the tractor for the first year if he runs the tractor for a total of $800 \mathrm{hr}$. Include hourly costs and depreciation.
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