Hello there. To solve this question, we'll have to plug the value of x in the function and evalute it;.
Given the function:
![f(x)=5.6e^(-0.46x)](https://img.qammunity.org/2023/formulas/mathematics/college/26z53m0i5b2xscqlrasar6cvlxlhn0c0gt.png)
We want to determine
![f(7.5)](https://img.qammunity.org/2023/formulas/mathematics/college/az7czfvvv265d79g7f1j815116hf8gucic.png)
With a calculator, we plug the value
![f(7.5)=5.6e^(-0.46\cdot7.5)=5.6e^(-3.45)](https://img.qammunity.org/2023/formulas/mathematics/college/privkf1zkkrzfnuz072m7uz4hbpi6qd1li.png)
And this is approximately equal to
![f(7.5)\approx0.17](https://img.qammunity.org/2023/formulas/mathematics/college/t5czaga9pj1t8fjixhh6tdr4i9dbijfcmx.png)
This is the value of the function.