Question

A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. Use exponential growth formula

Answer 1

Hello Shannonrodrigue. You can solve this by setting up an exponential growth equation.

$A = A_ob^t$
$3600 = 3000b^4$

Now we solve for b
$3600 = 3000b^4$
$\frac{3600}{3000} = \frac{3000b^{4}}{3000}$
$\frac{6}{5} = b^4$
$\sqrt[4]{\frac{6}{5}} = \sqrt[4]{b^4}$
$\sqrt[4]{\frac{6}{5}} = b$

Now that we have found b, we can use the equation $A = 3000b^t$ to predict how many bacteria will be present after 10 hours.
$b = \sqrt[4]{\frac{6}{5}}$
t = 10
$A = 3000b^t$
$A = 3000\sqrt[4]{\frac{6}{5}}^{10} = 4732.3228 = 4732$

Answer = 4732