in exponential rate vs at exponential rate

Some examples from the web:

• It's suffice to say that we reached a point where science and technology have advanced in such an exponential rate for so long... it may be way beyond our ability to regulate and control them.
• They have been expanding, urbanization has been expanding, at an exponential rate in the last 200 years so that by the second part of this century, the planet will be completely dominated by cities.
• ...deteriorate at an exponential rate from host to host.
• The quantity and quality of this trade is growing at an exponential rate.
• This is quite simply an exponential rate of growth.
• Miniaturization - we're shrinking the size of technology at an exponential rate, both wired and wireless.
• The incidence of allergies is increasing at an almost exponential rate at a time when other illnesses such as infections or sudden infant death syndrome are in decline.
• The last few years have seen the property market in China grow at an exponential rate, attracting large amounts of foreign capital.
• Notes with great concern the almost exponential rate of infection throughout the world;
• However, Hulk's gamma build-up is increasing at an exponential rate.
• But suffice to say that we reached the point where science and technology have advanced at such an exponential rate for so long, it may be way beyond our ability to regulate and control them.
• The fact is that, since the disastrous 1985 Schengen agreements abolishing the European Union's internal border controls, these two phenomena - which no one doubts are closely linked - have developed at an exponential rate.
• The evolution of web communities and hosted services such as social network services ('SNS') are a relatively recent phenomenon, with the number of users of these sites continuing to multiply at an exponential rate.
• The fair trade movement in Europe has grown at an exponential rate these past few years; more and more shops and points of sale are carrying fair trade products which in some cases can now even be found in supermarkets, involving millions of consumers.
• Nowadays, however, Flanders feels the need to reactivate this railway line, in view of the growing problems with container traffic in Flanders, the Netherlands and Germany, which is growing at an exponential rate.
• I is for the invasive species like the fire ants, the zebra mussels, broom grasses and pathogenic bacteria and viruses that are flooding every country, and at an exponential rate - that's the I.
• Control of this disease must be an essential objective for the European Union, also bearing in mind that the incidence of this disease is increasing at an exponential rate with age and that it doubles every 5 years from 75 years of age.
• Student loans are already a scam - impossible interest rates, exponential debt, easy access.
• We are seeing the crisis deepening in many developing countries, with unprecedented unemployment rates and exponential growth in government debt and budget deficits.
• They go to work; replicating, spreading like a virus, multiplying in exponentials.

Some examples from the web:

• ...deteriorate at an exponential rate from host to host.
• The quantity and quality of this trade is growing at an exponential rate.
• The incidence of allergies is increasing at an almost exponential rate at a time when other illnesses such as infections or sudden infant death syndrome are in decline.
• Miniaturization - we're shrinking the size of technology at an exponential rate, both wired and wireless.
• The last few years have seen the property market in China grow at an exponential rate, attracting large amounts of foreign capital.
• However, Hulk's gamma build-up is increasing at an exponential rate.
• The fact is that, since the disastrous 1985 Schengen agreements abolishing the European Union's internal border controls, these two phenomena - which no one doubts are closely linked - have developed at an exponential rate.
• But suffice to say that we reached the point where science and technology have advanced at such an exponential rate for so long, it may be way beyond our ability to regulate and control them.
• They have been expanding, urbanization has been expanding, at an exponential rate in the last 200 years so that by the second part of this century, the planet will be completely dominated by cities.
• The evolution of web communities and hosted services such as social network services ('SNS') are a relatively recent phenomenon, with the number of users of these sites continuing to multiply at an exponential rate.
• The fair trade movement in Europe has grown at an exponential rate these past few years; more and more shops and points of sale are carrying fair trade products which in some cases can now even be found in supermarkets, involving millions of consumers.
• Nowadays, however, Flanders feels the need to reactivate this railway line, in view of the growing problems with container traffic in Flanders, the Netherlands and Germany, which is growing at an exponential rate.
• I is for the invasive species like the fire ants, the zebra mussels, broom grasses and pathogenic bacteria and viruses that are flooding every country, and at an exponential rate - that's the I.
• Control of this disease must be an essential objective for the European Union, also bearing in mind that the incidence of this disease is increasing at an exponential rate with age and that it doubles every 5 years from 75 years of age.
• This is quite simply an exponential rate of growth.
• Notes with great concern the almost exponential rate of infection throughout the world;
• It's suffice to say that we reached a point where science and technology have advanced in such an exponential rate for so long... it may be way beyond our ability to regulate and control them.
• Student loans are already a scam - impossible interest rates, exponential debt, easy access.
• We are seeing the crisis deepening in many developing countries, with unprecedented unemployment rates and exponential growth in government debt and budget deficits.
• In other words, the rate of increase is exponential.