Question14 Mark for Review
The function $f(t)=60,000(2)^{\frac{t}{40}}$ gives the number of bacteria in a population $t$ minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
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Studdy Solution
Solve the equation for $t$.
Divide both sides by 60,000 to isolate the exponential term:
$$(2)^{\frac{t}{40}} = \frac{120,000}{60,000}$$ $$(2)^{\frac{t}{40}} = 2$$
Since $2^1 = 2$, we have:
$$\frac{t}{40} = 1$$
Multiply both sides by 40 to solve for $t$:
$$t = 40 \times 1$$ $$t = 40$$
It takes $\boxed{40}$ minutes for the number of bacteria to double.