Question

There are 100 bacteria in a jar. Every day, the number of bacteria increases 25%. In approximately how many days will there be 500 bactria in the jar? Pick the closest answer.
A. 3
B. 12
C. 10
D. 2
E. 7

Answer 1

Answer:

E. 7

Step-by-step explanation:

General form of exponential equation:  $y=ab^x$

where $a$ is the initial value, $b$ is the growth/decay rate, and $x$ is time.

Given:

• $a$ = 100 bacteria
• $b$ = 25% increase = 1.25
• $x$ = number of days

⇒ $y=100 \cdot 1.25^x$

If y = 500, then:

$\implies 500=100 \cdot 1.25^x$

$\implies 5=1.25^x$

$\implies \ln5=\ln1.25^x$

$\implies \ln5=x\ln1.25^$

$\implies x=\dfrac{\ln5}{\ln1.25}$

$\implies x=7.212567439...$

$\implies x \approx7$

Answer 2

Use compound interest formula

$\\ \rm\Rrightarrow P(1+r/100)^t=500$

$\\ \rm\Rrightarrow 100(1+0.25)^t=500$

$\\ \rm\Rrightarrow (1.25)^t=5$

$\\ \rm\Rrightarrow log(1.25)^t=log5$

$\\ \rm\Rrightarrow tlog1.25=log5$

$\\ \rm\Rrightarrow t(0.097)=0.3$

$\\ \rm\Rrightarrow t=3.3\approx 3$

Option A