Question

the elevator pitch math quiz
question 8 of 10: you hear a pitch where the founder says hell reach $30 million in sales in 5 years. his first - year sales are projected at $5 million. which is closest to the compound growth rate he is implying? the formula for compound growth is e = b×(1 + r)^t, where e is ending value, b is beginning value, r is rate of growth, and t is the amount of time.
a) - 10%
b) 14%
c) 56%
d) 298%

Explanation:

Step1: Substitute values into formula

Given $E = 30$ (ending value in millions), $B = 5$ (beginning value in millions), and $T=5$ (time in years). The formula $E = B\times(1 + R)^T$ becomes $30=5\times(1 + R)^5$.

Step2: Simplify the equation

Divide both sides of the equation by 5: $\frac{30}{5}=(1 + R)^5$, so $6=(1 + R)^5$.

Step3: Solve for $R$

Take the fifth - root of both sides: $1 + R = 6^{\frac{1}{5}}$. Calculate $6^{\frac{1}{5}}\approx1.431$. Then $R=1.431 - 1=0.431\approx43\%$. The closest value to $43\%$ among the options is $56\%$.

Answer:

c) 56%