Growth can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it grows by using t=25 minutes and $\frac{A_{0}}{A} =2$ or double the amount at that time. The first step we always take is to divide $A_0$ by A.

$[tex]\frac{A_{0}}{A}=e^{rt}\\2=e^{r(25)}$

$2=e^{(25)r}$

To solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 2=ln e^{(25)r}\\ln 2=25r (ln e)\\\frac{ln2}{25} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 25.

We solve with a calculator $\frac{ln2}{25} =r\\0.0277=r$

We change 0.0277 into a percent by multiplying by 100 to get 2.77% as the rate.

The equation is $A=A_0e^{0.0277t}$ .

We repeat the step above substituting A=5,000,000, $A_0$ =50, and r=0.02777. Then solve for t.

$5000000=50e^{0.0277t}\\\frac{5000000}{50} =e^{0.0277t}\\100000=e^{0.0277t}\\ln100000=lne^{0.0277t}\\ln100000=0.02777t(lne)\\\frac{ln100000}{0.0277} =t$

t=415.63 minutes

6 0

4 years ago

Emily earns extra spending money by babysitting children in her neighborhood. On Tuesday, she earned $16 for baby

Ipatiy [6.2K]

Answer:

The rate of change is 8

Step-by-step explanation:

put the 16 as the numerator then the 2 hours as the denominator then divide by 2 to get you 8 dollars for 1 hour

8 0

3 years ago

1. Simplify 1- |-1|

Hunter-Best [27]

1. Simplified is 0
2. Simplified is 6
3. Simplified is 12
4. Simplified is -4
5. Simplified is -1
6. Simplified is -1

4 0

2 years ago