Question

Evaluating an exponential function with base e that models a real-world situation

Answer 1

a) 19 m/s

b) 28 m/s

Step-by-step explanation:
`\begin{gathered} \text{Given function:} \\ v(t)\text{ = 51(}1-e^(-0.16t)) \\ \\ We\text{ find the values of v(t) with the given t values} \end{gathered}`

when t = 3 seconds

`\begin{gathered} v(t)\text{ = 51(}1-e^(-0.16(3))) \\ v(t)\text{ = 51(}1-e^(-0.16(3))) \\ v(t)\text{ =}51(1\text{ - 0.6188)} \\ v(t)\text{ = 19.4420 m/s} \\ \\ To\text{ the nearest whole number, v(t) = 19 m/s} \end{gathered}`

when t = 5 seconds

`\begin{gathered} v(t)\text{ = 51(}1-e^(-0.16(5))) \\ v(t)\text{ = 51(}1-0.4493) \\ v(t)\text{ = 28.0842 m/s} \\ \\ To\text{ the nearest whole number, v(t) = 28 m/s} \end{gathered}`