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Gnesinka [82]
3 years ago
12

The population of a certain city grows exponentially. When the city was founded, it only had 1000 residents. After 1 year the ci

ty had 1050 residents. Write an equation that models the population y of the city after x years.
Mathematics
1 answer:
mihalych1998 [28]3 years ago
6 0

Our function is something like

y=ae^{bx}

When the city was founded, 0 years have passed. So, we want

y(0)=1000 \iff ae^{0x}=1000 \iff a\cdot 1 = 1000 \iff a=1000

So, we can update our function: now we know that it will be something like

y=1000e^{bx}

Similarly, we have to impose y(1)=1050. Since

y(1)=1000e^{b\cdot 1}=1000e^b

we have to impose

1000e^b=1050 \iff e^b = 1.05 \iff b = \ln(1.05)

So, our function is

y=1000e^{\ln(1.05)x}

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