Exponential growth problem solved with logarithms

Exponential Growth Solution
Use: *f(t) = f(0) e^kt* k is constant; t is time. First find value of the constant k. Enter value for 2 days into: f(t) = f(0) e^kt 2,000,000 = 1,000,000 e^k2 2 = e^k2 ln2 = 2 k k = $\frac{ln 2}{2}$ Now use k in original formula with 7 days f(t) = f(0) e^kt f(7) = 1,000,000 e^{( $\frac{ln 2}{2}$ * 7)} f(7) = 1,000,000 e^{(ln2 * $\frac{7}{2}$ )} f(7) = 1,000,000 * 2^7/2 f(7) = 1,000,000 * 11.313709 ≈ 11,313,709
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Exponential Growth
Solution

Use: f(t) = f(0) e^kt k is constant; t is time.
First find value of the constant k.
Enter value for 2 days into: f(t) = f(0) e^kt
2,000,000 = 1,000,000 e^k2
2 = e^k2
ln2 = 2 k
k = $\frac{ln 2}{2}$

Now use k in original formula with 7 days
f(t) = f(0) e^kt
f(7) = 1,000,000 e^{( $\frac{ln 2}{2}$ * 7)}
f(7) = 1,000,000 e^{(ln2 * $\frac{7}{2}$ )}
f(7) = 1,000,000 * 2^7/2
f(7) = 1,000,000 * 11.313709 ≈ 11,313,709

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Exponential GrowthSolution

Exponential Growth
Solution