Need help finding required Propellant Fraction for equation

[BilboBombadillo]

Homework Statement

Consider a cryogenic chemical propulsion system with Isp (specific impulse) = 450 s
Enter the required propellant fraction as a proportion with at least two decimal places.

The ΔVelocity is provided. ΔV = 9.6 km/s

Homework Equations

Rocket equation:
ΔV = V_ex x Ln (initial mass/final mass)

The Attempt at a Solution

I'm atrocious at math, yet this question has come may way nonetheless. Do I just reverse the standard rocket equation one uses to find the Delta Velocity?
Propellant/final mass = ΔV x Isp?
I need smart folk.

 

[Mark44]

Homework Statement

Consider a cryogenic chemical propulsion system with Isp (specific impulse) = 450 s
Enter the required propellant fraction as a proportion with at least two decimal places.

The ΔVelocity is provided. ΔV = 9.6 km/s

Homework Equations

Rocket equation:
ΔV = V_ex x Ln (initial mass/final mass)

The Attempt at a Solution

I'm atrocious at math, yet this question has come may way nonetheless. Do I just reverse the standard rocket equation one uses to find the Delta Velocity?
Propellant/final mass = ΔV x Isp?
I need smart folk.

In the rocket equation you listed, where does I_sp fit in? Is there another relevant equation, or perhaps one that is more relevant to your problem?

 

[BilboBombadillo]

Apologies I forgot the actual equation. The rocket equation I figured was necessary anyway, as no mass information is provided.
Here:
Propellant Fraction:
m_prop/m_i = 1 - exp(-ΔV/V_ex)

 

[BilboBombadillo]

I_sp is part of the Exhaust velocity equation
V_ex = g₀ I_sp
In fact, I think a better question would be - How does one input exp(-ΔV/V_ex) on a calculator?

 

[Mark44]

I_sp is part of the Exhaust velocity equation
V_ex = g₀ I_sp
In fact, I think a better question would be - How does one input exp(-ΔV/V_ex) on a calculator?

It depends on the kind of calculator you have. If it's a standard scientific calculator, enter ΔV, divide by V, change the sign (usually marked +/-), and then hit the e^x button. Some of the fancier calculators these days allow you to enter the formula in the display.